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href="/w/index.php?title=%CE%95%CE%B9%CE%B4%CE%B9%CE%BA%CF%8C:%CE%94%CE%B7%CE%BC%CE%B9%CE%BF%CF%85%CF%81%CE%B3%CE%AF%CE%B1%CE%9B%CE%BF%CE%B3%CE%B1%CF%81%CE%B9%CE%B1%CF%83%CE%BC%CE%BF%CF%8D&returnto=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD" title="Σας ενθαρρύνουμε να δημιουργήσετε ένα λογαριασμό και να συνδεθείτε· ωστόσο, δεν είναι υποχρεωτικό"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Δημιουργία λογαριασμού</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%CE%95%CE%B9%CE%B4%CE%B9%CE%BA%CF%8C:%CE%A3%CF%8D%CE%BD%CE%B4%CE%B5%CF%83%CE%B7%CE%A7%CF%81%CE%AE%CF%83%CF%84%CE%B7&returnto=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD" title="Σας ενθαρρύνουμε να συνδεθείτε· ωστόσο, δεν είναι υποχρεωτικό [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Σύνδεση</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Σελίδες για αποσυνδεμένους συντάκτες <a href="/wiki/%CE%92%CE%BF%CE%AE%CE%B8%CE%B5%CE%B9%CE%B1:%CE%95%CE%B9%CF%83%CE%B1%CE%B3%CF%89%CE%B3%CE%AE" aria-label="Μάθετε περισσότερα σχετικά με την επεξεργασία"><span>μάθετε περισσότερα</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/%CE%95%CE%B9%CE%B4%CE%B9%CE%BA%CF%8C:%CE%9F%CE%B9%CE%A3%CF%85%CE%BD%CE%B5%CE%B9%CF%83%CF%86%CE%BF%CF%81%CE%AD%CF%82%CE%9C%CE%BF%CF%85" title="Μια λίστα με τις επεξεργασίες που έγιναν από αυτή τη διεύθυνση IP [y]" accesskey="y"><span>Συνεισφορές</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%CE%95%CE%B9%CE%B4%CE%B9%CE%BA%CF%8C:%CE%97%CE%A3%CF%85%CE%B6%CE%AE%CF%84%CE%B7%CF%83%CE%AE%CE%9C%CE%BF%CF%85" title="Συζήτηση σχετικά με τις αλλαγές που έγιναν από αυτή τη διεύθυνση IP [n]" accesskey="n"><span>Συζήτηση για αυτή την IP</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"><div id="mw-dismissablenotice-anonplace"></div><script>(function(){var node=document.getElementById("mw-dismissablenotice-anonplace");if(node){node.outerHTML="\u003Cdiv class=\"mw-dismissable-notice\"\u003E\u003Cdiv class=\"mw-dismissable-notice-close\"\u003E[\u003Ca tabindex=\"0\" role=\"button\"\u003Eκλείσιμο\u003C/a\u003E]\u003C/div\u003E\u003Cdiv class=\"mw-dismissable-notice-body\"\u003E\u003C!-- CentralNotice --\u003E\u003Cdiv id=\"localNotice\" data-nosnippet=\"\"\u003E\u003Cdiv class=\"sitenotice\" lang=\"el\" dir=\"ltr\"\u003E\u003Cdiv class=\"plainlinks\" style=\"border: 1px solid #ddd; margin: 0 0 3px;\"\u003E\n\u003Cdiv class=\"nomobile\" style=\"float:right\"\u003E\u003Cspan typeof=\"mw:File\"\u003E\u003Ca 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vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Περιεχόμενα</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">μετακίνηση στην πλαϊνή μπάρα</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">απόκρυψη</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Αρχή</div> </a> </li> <li id="toc-Λίστα_τύπων_υπολογισμού_εμβαδού_διαφόρων_σχημάτων" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Λίστα_τύπων_υπολογισμού_εμβαδού_διαφόρων_σχημάτων"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Λίστα τύπων υπολογισμού εμβαδού διαφόρων σχημάτων</span> </div> </a> <button aria-controls="toc-Λίστα_τύπων_υπολογισμού_εμβαδού_διαφόρων_σχημάτων-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Εναλλαγή Λίστα τύπων υπολογισμού εμβαδού διαφόρων σχημάτων υποενότητας</span> </button> <ul id="toc-Λίστα_τύπων_υπολογισμού_εμβαδού_διαφόρων_σχημάτων-sublist" class="vector-toc-list"> <li id="toc-Τρίγωνο" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Τρίγωνο"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Τρίγωνο</span> </div> </a> <ul id="toc-Τρίγωνο-sublist" class="vector-toc-list"> <li id="toc-Ειδικά_τρίγωνα" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Ειδικά_τρίγωνα"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1.1</span> <span>Ειδικά τρίγωνα</span> </div> </a> <ul id="toc-Ειδικά_τρίγωνα-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Τετράπλευρο" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Τετράπλευρο"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Τετράπλευρο</span> </div> </a> <ul id="toc-Τετράπλευρο-sublist" class="vector-toc-list"> <li id="toc-Ειδικά_τετράπλευρα" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Ειδικά_τετράπλευρα"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2.1</span> <span>Ειδικά τετράπλευρα</span> </div> </a> <ul id="toc-Ειδικά_τετράπλευρα-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Κανονικό_πολύγωνο" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Κανονικό_πολύγωνο"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Κανονικό πολύγωνο</span> </div> </a> <ul id="toc-Κανονικό_πολύγωνο-sublist" class="vector-toc-list"> <li id="toc-Ειδικές_περιπτώσεις" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Ειδικές_περιπτώσεις"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3.1</span> <span>Ειδικές περιπτώσεις</span> </div> </a> <ul id="toc-Ειδικές_περιπτώσεις-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Κύκλος_και_κυκλικός_τομέας" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Κύκλος_και_κυκλικός_τομέας"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Κύκλος και κυκλικός τομέας</span> </div> </a> <ul id="toc-Κύκλος_και_κυκλικός_τομέας-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Επιφάνεια_γεωματερικών_στερεών" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Επιφάνεια_γεωματερικών_στερεών"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Επιφάνεια γεωματερικών στερεών</span> </div> </a> <button aria-controls="toc-Επιφάνεια_γεωματερικών_στερεών-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Εναλλαγή Επιφάνεια γεωματερικών στερεών υποενότητας</span> </button> <ul id="toc-Επιφάνεια_γεωματερικών_στερεών-sublist" class="vector-toc-list"> <li id="toc-Κύλινδρος" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Κύλινδρος"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Κύλινδρος</span> </div> </a> <ul id="toc-Κύλινδρος-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Σφαίρα" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Σφαίρα"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Σφαίρα</span> </div> </a> <ul id="toc-Σφαίρα-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Πυραμίδα" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Πυραμίδα"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Πυραμίδα</span> </div> </a> <ul id="toc-Πυραμίδα-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Κώνος" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Κώνος"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Κώνος</span> </div> </a> <ul id="toc-Κώνος-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Μεταξύ_όμοιων_σχημάτων" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Μεταξύ_όμοιων_σχημάτων"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Μεταξύ όμοιων σχημάτων</span> </div> </a> <ul id="toc-Μεταξύ_όμοιων_σχημάτων-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Δείτε_επίσης" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Δείτε_επίσης"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Δείτε επίσης</span> </div> </a> <ul id="toc-Δείτε_επίσης-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Περαιτέρω_ανάγνωση" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Περαιτέρω_ανάγνωση"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Περαιτέρω ανάγνωση</span> </div> </a> <button aria-controls="toc-Περαιτέρω_ανάγνωση-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Εναλλαγή Περαιτέρω ανάγνωση υποενότητας</span> </button> <ul id="toc-Περαιτέρω_ανάγνωση-sublist" class="vector-toc-list"> <li id="toc-Ελληνικά_άρθρα" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ελληνικά_άρθρα"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Ελληνικά άρθρα</span> </div> </a> <ul id="toc-Ελληνικά_άρθρα-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ξενόγλωσσα_άρθρα" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ξενόγλωσσα_άρθρα"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Ξενόγλωσσα άρθρα</span> </div> </a> <ul id="toc-Ξενόγλωσσα_άρθρα-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Παραπομπές" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Παραπομπές"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Παραπομπές</span> </div> </a> <ul id="toc-Παραπομπές-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Περιεχόμενα" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Πίνακας Περιεχομένων" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Εναλλαγή του πίνακα περιεχομένων" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Εναλλαγή του πίνακα περιεχομένων</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Εμβαδόν</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Μεταβείτε σε ένα λήμμα σε άλλη γλώσσα. Διαθέσιμο σε 165 γλώσσες" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-165" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">165 γλώσσες</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Oppervlakte" title="Oppervlakte – Αφρικάανς" lang="af" hreflang="af" data-title="Oppervlakte" data-language-autonym="Afrikaans" data-language-local-name="Αφρικάανς" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Fl%C3%A4cheninhalt" title="Flächeninhalt – Γερμανικά Ελβετίας" lang="gsw" hreflang="gsw" data-title="Flächeninhalt" data-language-autonym="Alemannisch" data-language-local-name="Γερμανικά Ελβετίας" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Aria" title="Aria – Αραγονικά" lang="an" hreflang="an" data-title="Aria" data-language-autonym="Aragonés" data-language-local-name="Αραγονικά" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-anp mw-list-item"><a href="https://anp.wikipedia.org/wiki/%E0%A4%95%E0%A5%8D%E0%A4%B7%E0%A5%87%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%AB%E0%A4%B2" title="क्षेत्रफल – Ανγκικά" lang="anp" hreflang="anp" data-title="क्षेत्रफल" data-language-autonym="अंगिका" data-language-local-name="Ανγκικά" class="interlanguage-link-target"><span>अंगिका</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%B3%D8%A7%D8%AD%D8%A9" title="مساحة – Αραβικά" lang="ar" hreflang="ar" data-title="مساحة" data-language-autonym="العربية" data-language-local-name="Αραβικά" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-arc mw-list-item"><a href="https://arc.wikipedia.org/wiki/%DC%AB%DC%9B%DC%9D%DC%9A%DC%98%DC%AC%DC%90" title="ܫܛܝܚܘܬܐ – Αραμαϊκά" lang="arc" hreflang="arc" data-title="ܫܛܝܚܘܬܐ" data-language-autonym="ܐܪܡܝܐ" data-language-local-name="Αραμαϊκά" class="interlanguage-link-target"><span>ܐܪܡܝܐ</span></a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D8%AA%D9%8A%D8%B3%D8%A7%D8%B9" title="تيساع – Moroccan Arabic" lang="ary" hreflang="ary" data-title="تيساع" data-language-autonym="الدارجة" data-language-local-name="Moroccan Arabic" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D9%85%D8%B3%D8%A7%D8%AD%D9%87" title="مساحه – Egyptian Arabic" lang="arz" hreflang="arz" data-title="مساحه" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%95%E0%A7%8D%E0%A6%B7%E0%A7%87%E0%A6%A4%E0%A7%8D%E0%A7%B0%E0%A6%AB%E0%A6%B2" title="ক্ষেত্ৰফল – Ασαμικά" lang="as" hreflang="as" data-title="ক্ষেত্ৰফল" data-language-autonym="অসমীয়া" data-language-local-name="Ασαμικά" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/%C3%81rea_(xeometr%C3%ADa)" title="Área (xeometría) – Αστουριανά" lang="ast" hreflang="ast" data-title="Área (xeometría)" data-language-autonym="Asturianu" data-language-local-name="Αστουριανά" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-av mw-list-item"><a href="https://av.wikipedia.org/wiki/%D0%9F%D0%BB%D0%BE%D1%89%D0%B0%D0%B4%D1%8C" title="Площадь – Αβαρικά" lang="av" hreflang="av" data-title="Площадь" data-language-autonym="Авар" data-language-local-name="Αβαρικά" class="interlanguage-link-target"><span>Авар</span></a></li><li class="interlanguage-link interwiki-awa mw-list-item"><a href="https://awa.wikipedia.org/wiki/%E0%A4%95%E0%A5%8D%E0%A4%B7%E0%A5%87%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%AB%E0%A4%B2" title="क्षेत्रफल – Αγουαντί" lang="awa" hreflang="awa" data-title="क्षेत्रफल" data-language-autonym="अवधी" data-language-local-name="Αγουαντί" class="interlanguage-link-target"><span>अवधी</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Sah%C9%99_(%C3%B6l%C3%A7%C3%BC_parametri)" title="Sahə (ölçü parametri) – Αζερμπαϊτζανικά" lang="az" hreflang="az" data-title="Sahə (ölçü parametri)" data-language-autonym="Azərbaycanca" data-language-local-name="Αζερμπαϊτζανικά" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D9%85%D8%B3%D8%A7%D8%AD%D8%AA" title="مساحت – South Azerbaijani" lang="azb" hreflang="azb" data-title="مساحت" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%9C%D0%B0%D0%B9%D2%99%D0%B0%D0%BD" title="Майҙан – Μπασκίρ" lang="ba" hreflang="ba" data-title="Майҙан" data-language-autonym="Башҡортса" data-language-local-name="Μπασκίρ" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Fl%C3%A4chn" title="Flächn – Bavarian" lang="bar" hreflang="bar" data-title="Flächn" data-language-autonym="Boarisch" data-language-local-name="Bavarian" class="interlanguage-link-target"><span>Boarisch</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Pluots" title="Pluots – Samogitian" lang="sgs" hreflang="sgs" data-title="Pluots" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Hiwas" title="Hiwas – Central Bikol" lang="bcl" hreflang="bcl" data-title="Hiwas" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9F%D0%BB%D0%BE%D1%88%D1%87%D0%B0" title="Плошча – Λευκορωσικά" lang="be" hreflang="be" data-title="Плошча" data-language-autonym="Беларуская" data-language-local-name="Λευκορωσικά" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9F%D0%BB%D0%BE%D1%88%D1%87%D0%B0" title="Плошча – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Плошча" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9F%D0%BB%D0%BE%D1%89" title="Площ – Βουλγαρικά" lang="bg" hreflang="bg" data-title="Площ" data-language-autonym="Български" data-language-local-name="Βουλγαρικά" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%95%E0%A5%8D%E0%A4%B7%E0%A5%87%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%AB%E0%A4%B2" title="क्षेत्रफल – Bhojpuri" lang="bh" hreflang="bh" data-title="क्षेत्रफल" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target"><span>भोजपुरी</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%95%E0%A7%8D%E0%A6%B7%E0%A7%87%E0%A6%A4%E0%A7%8D%E0%A6%B0%E0%A6%AB%E0%A6%B2" title="ক্ষেত্রফল – Βεγγαλικά" lang="bn" hreflang="bn" data-title="ক্ষেত্রফল" data-language-autonym="বাংলা" data-language-local-name="Βεγγαλικά" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Gorread" title="Gorread – Βρετονικά" lang="br" hreflang="br" data-title="Gorread" data-language-autonym="Brezhoneg" data-language-local-name="Βρετονικά" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Povr%C5%A1ina" title="Površina – Βοσνιακά" lang="bs" hreflang="bs" data-title="Površina" data-language-autonym="Bosanski" data-language-local-name="Βοσνιακά" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-btm mw-list-item"><a href="https://btm.wikipedia.org/wiki/Bolak" title="Bolak – Batak Mandailing" lang="btm" hreflang="btm" data-title="Bolak" data-language-autonym="Batak Mandailing" data-language-local-name="Batak Mandailing" class="interlanguage-link-target"><span>Batak Mandailing</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/%C3%80rea" title="Àrea – Καταλανικά" lang="ca" hreflang="ca" data-title="Àrea" data-language-autonym="Català" data-language-local-name="Καταλανικά" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cdo mw-list-item"><a href="https://cdo.wikipedia.org/wiki/Mi%C3%AAng-c%C3%A9k" title="Miêng-cék – Mindong" lang="cdo" hreflang="cdo" data-title="Miêng-cék" data-language-autonym="閩東語 / Mìng-dĕ̤ng-ngṳ̄" data-language-local-name="Mindong" class="interlanguage-link-target"><span>閩東語 / Mìng-dĕ̤ng-ngṳ̄</span></a></li><li class="interlanguage-link interwiki-ce mw-list-item"><a href="https://ce.wikipedia.org/wiki/%D0%9C%D0%B0%D0%B9%D0%B4%D0%B0" title="Майда – Τσετσενικά" lang="ce" hreflang="ce" data-title="Майда" data-language-autonym="Нохчийн" data-language-local-name="Τσετσενικά" class="interlanguage-link-target"><span>Нохчийн</span></a></li><li class="interlanguage-link interwiki-ceb mw-list-item"><a href="https://ceb.wikipedia.org/wiki/Langyab" title="Langyab – Σεμπουάνο" lang="ceb" hreflang="ceb" data-title="Langyab" data-language-autonym="Cebuano" data-language-local-name="Σεμπουάνο" class="interlanguage-link-target"><span>Cebuano</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DA%95%D9%88%D9%88%D8%A8%DB%95%D8%B1" title="ڕووبەر – Κεντρικά Κουρδικά" lang="ckb" hreflang="ckb" data-title="ڕووبەر" data-language-autonym="کوردی" data-language-local-name="Κεντρικά Κουρδικά" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Obsah" title="Obsah – Τσεχικά" lang="cs" hreflang="cs" data-title="Obsah" data-language-autonym="Čeština" data-language-local-name="Τσεχικά" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cu mw-list-item"><a href="https://cu.wikipedia.org/wiki/%D0%9F%D1%80%D0%BE%D1%81%D1%82%D1%80%D0%B0%D0%BD%D0%B8%D1%A5" title="Пространиѥ – Εκκλησιαστικά Σλαβικά" lang="cu" hreflang="cu" data-title="Пространиѥ" data-language-autonym="Словѣньскъ / ⰔⰎⰑⰂⰡⰐⰠⰔⰍⰟ" data-language-local-name="Εκκλησιαστικά Σλαβικά" class="interlanguage-link-target"><span>Словѣньскъ / ⰔⰎⰑⰂⰡⰐⰠⰔⰍⰟ</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9B%D0%B0%D0%BF%D1%82%C4%83%D0%BA" title="Лаптăк – Τσουβασικά" lang="cv" hreflang="cv" data-title="Лаптăк" data-language-autonym="Чӑвашла" data-language-local-name="Τσουβασικά" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Arwynebedd" title="Arwynebedd – Ουαλικά" lang="cy" hreflang="cy" data-title="Arwynebedd" data-language-autonym="Cymraeg" data-language-local-name="Ουαλικά" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Areal" title="Areal – Δανικά" lang="da" hreflang="da" data-title="Areal" data-language-autonym="Dansk" data-language-local-name="Δανικά" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Fl%C3%A4cheninhalt" title="Flächeninhalt – Γερμανικά" lang="de" hreflang="de" data-title="Flächeninhalt" data-language-autonym="Deutsch" data-language-local-name="Γερμανικά" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-diq mw-list-item"><a href="https://diq.wikipedia.org/wiki/Erd" title="Erd – Dimli" lang="diq" hreflang="diq" data-title="Erd" data-language-autonym="Zazaki" data-language-local-name="Dimli" class="interlanguage-link-target"><span>Zazaki</span></a></li><li class="interlanguage-link interwiki-dsb mw-list-item"><a href="https://dsb.wikipedia.org/wiki/Wop%C5%9Bimje%C5%9Be_p%C5%82oni" title="Wopśimjeśe płoni – Κάτω Σορβικά" lang="dsb" hreflang="dsb" data-title="Wopśimjeśe płoni" data-language-autonym="Dolnoserbski" data-language-local-name="Κάτω Σορβικά" class="interlanguage-link-target"><span>Dolnoserbski</span></a></li><li class="interlanguage-link interwiki-dv mw-list-item"><a href="https://dv.wikipedia.org/wiki/%DE%87%DE%A6%DE%86%DE%A6%DE%89%DE%A8%DE%82%DE%B0" title="އަކަމިން – Ντιβέχι" lang="dv" hreflang="dv" data-title="އަކަމިން" data-language-autonym="ދިވެހިބަސް" data-language-local-name="Ντιβέχι" class="interlanguage-link-target"><span>ދިވެހިބަސް</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Area" title="Area – Αγγλικά" lang="en" hreflang="en" data-title="Area" data-language-autonym="English" data-language-local-name="Αγγλικά" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Areo" title="Areo – Εσπεράντο" lang="eo" hreflang="eo" data-title="Areo" data-language-autonym="Esperanto" data-language-local-name="Εσπεράντο" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/%C3%81rea" title="Área – Ισπανικά" lang="es" hreflang="es" data-title="Área" data-language-autonym="Español" data-language-local-name="Ισπανικά" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Pindala" title="Pindala – Εσθονικά" lang="et" hreflang="et" data-title="Pindala" data-language-autonym="Eesti" data-language-local-name="Εσθονικά" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Azalera" title="Azalera – Βασκικά" lang="eu" hreflang="eu" data-title="Azalera" data-language-autonym="Euskara" data-language-local-name="Βασκικά" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D8%B3%D8%A7%D8%AD%D8%AA" title="مساحت – Περσικά" lang="fa" hreflang="fa" data-title="مساحت" data-language-autonym="فارسی" data-language-local-name="Περσικά" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Pinta-ala" title="Pinta-ala – Φινλανδικά" lang="fi" hreflang="fi" data-title="Pinta-ala" data-language-autonym="Suomi" data-language-local-name="Φινλανδικά" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Pindala" title="Pindala – Võro" lang="vro" hreflang="vro" data-title="Pindala" data-language-autonym="Võro" data-language-local-name="Võro" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-fj mw-list-item"><a href="https://fj.wikipedia.org/wiki/Iwasewase" title="Iwasewase – Φίτζι" lang="fj" hreflang="fj" data-title="Iwasewase" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="Φίτζι" class="interlanguage-link-target"><span>Na Vosa Vakaviti</span></a></li><li class="interlanguage-link interwiki-fo mw-list-item"><a href="https://fo.wikipedia.org/wiki/V%C3%ADdd" title="Vídd – Φεροϊκά" lang="fo" hreflang="fo" data-title="Vídd" data-language-autonym="Føroyskt" data-language-local-name="Φεροϊκά" class="interlanguage-link-target"><span>Føroyskt</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Aire_(g%C3%A9om%C3%A9trie)" title="Aire (géométrie) – Γαλλικά" lang="fr" hreflang="fr" data-title="Aire (géométrie)" data-language-autonym="Français" data-language-local-name="Γαλλικά" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Areaal_(Miat)" title="Areaal (Miat) – Βόρεια Φριζιανά" lang="frr" hreflang="frr" data-title="Areaal (Miat)" data-language-autonym="Nordfriisk" data-language-local-name="Βόρεια Φριζιανά" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-fy mw-list-item"><a href="https://fy.wikipedia.org/wiki/Oerflak" title="Oerflak – Δυτικά Φριζικά" lang="fy" hreflang="fy" data-title="Oerflak" data-language-autonym="Frysk" data-language-local-name="Δυτικά Φριζικά" class="interlanguage-link-target"><span>Frysk</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E9%9D%A2%E7%A9%8D" title="面積 – Gan" lang="gan" hreflang="gan" data-title="面積" data-language-autonym="贛語" data-language-local-name="Gan" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/Farsaingeachd" title="Farsaingeachd – Σκωτικά Κελτικά" lang="gd" hreflang="gd" data-title="Farsaingeachd" data-language-autonym="Gàidhlig" data-language-local-name="Σκωτικά Κελτικά" class="interlanguage-link-target"><span>Gàidhlig</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/%C3%81rea" title="Área – Γαλικιανά" lang="gl" hreflang="gl" data-title="Área" data-language-autonym="Galego" data-language-local-name="Γαλικιανά" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gn mw-list-item"><a href="https://gn.wikipedia.org/wiki/Tendaha" title="Tendaha – Γκουαρανί" lang="gn" hreflang="gn" data-title="Tendaha" data-language-autonym="Avañe'ẽ" data-language-local-name="Γκουαρανί" class="interlanguage-link-target"><span>Avañe'ẽ</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%95%E0%AB%8D%E0%AA%B7%E0%AB%87%E0%AA%A4%E0%AB%8D%E0%AA%B0%E0%AA%AB%E0%AA%B3" title="ક્ષેત્રફળ – Γκουτζαρατικά" lang="gu" hreflang="gu" data-title="ક્ષેત્રફળ" data-language-autonym="ગુજરાતી" data-language-local-name="Γκουτζαρατικά" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-gv mw-list-item"><a href="https://gv.wikipedia.org/wiki/Eaghtyr" title="Eaghtyr – Μανξ" lang="gv" hreflang="gv" data-title="Eaghtyr" data-language-autonym="Gaelg" data-language-local-name="Μανξ" class="interlanguage-link-target"><span>Gaelg</span></a></li><li class="interlanguage-link interwiki-hak mw-list-item"><a href="https://hak.wikipedia.org/wiki/Mien-chit" title="Mien-chit – Hakka Chinese" lang="hak" hreflang="hak" data-title="Mien-chit" data-language-autonym="客家語 / Hak-kâ-ngî" data-language-local-name="Hakka Chinese" class="interlanguage-link-target"><span>客家語 / Hak-kâ-ngî</span></a></li><li class="interlanguage-link interwiki-haw mw-list-item"><a href="https://haw.wikipedia.org/wiki/%CA%BBAlea" title="ʻAlea – Χαβαϊκά" lang="haw" hreflang="haw" data-title="ʻAlea" data-language-autonym="Hawaiʻi" data-language-local-name="Χαβαϊκά" class="interlanguage-link-target"><span>Hawaiʻi</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A9%D7%98%D7%97" title="שטח – Εβραϊκά" lang="he" hreflang="he" data-title="שטח" data-language-autonym="עברית" data-language-local-name="Εβραϊκά" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%95%E0%A5%8D%E0%A4%B7%E0%A5%87%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%AB%E0%A4%B2" title="क्षेत्रफल – Χίντι" lang="hi" hreflang="hi" data-title="क्षेत्रफल" data-language-autonym="हिन्दी" data-language-local-name="Χίντι" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Area" title="Area – Fiji Hindi" lang="hif" hreflang="hif" data-title="Area" data-language-autonym="Fiji Hindi" data-language-local-name="Fiji Hindi" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Povr%C5%A1ina" title="Površina – Κροατικά" lang="hr" hreflang="hr" data-title="Površina" data-language-autonym="Hrvatski" data-language-local-name="Κροατικά" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hsb mw-list-item"><a href="https://hsb.wikipedia.org/wiki/Wobsah_p%C5%99estrjenje" title="Wobsah přestrjenje – Άνω Σορβικά" lang="hsb" hreflang="hsb" data-title="Wobsah přestrjenje" data-language-autonym="Hornjoserbsce" data-language-local-name="Άνω Σορβικά" class="interlanguage-link-target"><span>Hornjoserbsce</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Ter%C3%BClet_(matematika)" title="Terület (matematika) – Ουγγρικά" lang="hu" hreflang="hu" data-title="Terület (matematika)" data-language-autonym="Magyar" data-language-local-name="Ουγγρικά" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%84%D5%A1%D5%AF%D5%A5%D6%80%D5%A5%D5%BD" title="Մակերես – Αρμενικά" lang="hy" hreflang="hy" data-title="Մակերես" data-language-autonym="Հայերեն" data-language-local-name="Αρμενικά" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Area" title="Area – Ιντερλίνγκουα" lang="ia" hreflang="ia" data-title="Area" data-language-autonym="Interlingua" data-language-local-name="Ιντερλίνγκουα" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Luas" title="Luas – Ινδονησιακά" lang="id" hreflang="id" data-title="Luas" data-language-autonym="Bahasa Indonesia" data-language-local-name="Ινδονησιακά" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ilo mw-list-item"><a href="https://ilo.wikipedia.org/wiki/Kalawa" title="Kalawa – Ιλόκο" lang="ilo" hreflang="ilo" data-title="Kalawa" data-language-autonym="Ilokano" data-language-local-name="Ιλόκο" class="interlanguage-link-target"><span>Ilokano</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Areo" title="Areo – Ίντο" lang="io" hreflang="io" data-title="Areo" data-language-autonym="Ido" data-language-local-name="Ίντο" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Flatarm%C3%A1l" title="Flatarmál – Ισλανδικά" lang="is" hreflang="is" data-title="Flatarmál" data-language-autonym="Íslenska" data-language-local-name="Ισλανδικά" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Area" title="Area – Ιταλικά" lang="it" hreflang="it" data-title="Area" data-language-autonym="Italiano" data-language-local-name="Ιταλικά" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E9%9D%A2%E7%A9%8D" title="面積 – Ιαπωνικά" lang="ja" hreflang="ja" data-title="面積" data-language-autonym="日本語" data-language-local-name="Ιαπωνικά" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Ieria" title="Ieria – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Ieria" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Jembar" title="Jembar – Ιαβανικά" lang="jv" hreflang="jv" data-title="Jembar" data-language-autonym="Jawa" data-language-local-name="Ιαβανικά" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A4%E1%83%90%E1%83%A0%E1%83%97%E1%83%9D%E1%83%91%E1%83%98" title="ფართობი – Γεωργιανά" lang="ka" hreflang="ka" data-title="ფართობი" data-language-autonym="ქართული" data-language-local-name="Γεωργιανά" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Tajumma" title="Tajumma – Καμπίλε" lang="kab" hreflang="kab" data-title="Tajumma" data-language-autonym="Taqbaylit" data-language-local-name="Καμπίλε" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-kbd mw-list-item"><a href="https://kbd.wikipedia.org/wiki/%D0%A9%D3%80%D1%8B%D0%BF%D3%80%D1%8D_%D0%B8%D0%BD%D0%B0%D0%B3%D1%8A" title="ЩӀыпӀэ инагъ – Καμπαρντιανά" lang="kbd" hreflang="kbd" data-title="ЩӀыпӀэ инагъ" data-language-autonym="Адыгэбзэ" data-language-local-name="Καμπαρντιανά" class="interlanguage-link-target"><span>Адыгэбзэ</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%90%D1%83%D0%B4%D0%B0%D0%BD_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F)" title="Аудан (геометрия) – Καζακικά" lang="kk" hreflang="kk" data-title="Аудан (геометрия)" data-language-autonym="Қазақша" data-language-local-name="Καζακικά" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%80%E1%9F%92%E1%9E%9A%E1%9E%9B%E1%9E%B6%E1%9E%95%E1%9F%92%E1%9E%91%E1%9F%83" title="ក្រលាផ្ទៃ – Χμερ" lang="km" hreflang="km" data-title="ក្រលាផ្ទៃ" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="Χμερ" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%84%93%EC%9D%B4" title="넓이 – Κορεατικά" lang="ko" hreflang="ko" data-title="넓이" data-language-autonym="한국어" data-language-local-name="Κορεατικά" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-krc mw-list-item"><a href="https://krc.wikipedia.org/wiki/%D0%9C%D0%B0%D0%B9%D0%B4%D0%B0%D0%BD%D0%BB%D1%8B%D0%BA%D1%8A" title="Майданлыкъ – Καρατσάι-Μπαλκάρ" lang="krc" hreflang="krc" data-title="Майданлыкъ" data-language-autonym="Къарачай-малкъар" data-language-local-name="Καρατσάι-Μπαλκάρ" class="interlanguage-link-target"><span>Къарачай-малкъар</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/R%C3%BBerd" title="Rûerd – Κουρδικά" lang="ku" hreflang="ku" data-title="Rûerd" data-language-autonym="Kurdî" data-language-local-name="Κουρδικά" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-kw mw-list-item"><a href="https://kw.wikipedia.org/wiki/Enep_(fysegieth)" title="Enep (fysegieth) – Κορνουαλικά" lang="kw" hreflang="kw" data-title="Enep (fysegieth)" data-language-autonym="Kernowek" data-language-local-name="Κορνουαλικά" class="interlanguage-link-target"><span>Kernowek</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%90%D1%8F%D0%BD%D1%82" title="Аянт – Κιργιζικά" lang="ky" hreflang="ky" data-title="Аянт" data-language-autonym="Кыргызча" data-language-local-name="Κιργιζικά" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Area_(geometria)" title="Area (geometria) – Λατινικά" lang="la" hreflang="la" data-title="Area (geometria)" data-language-autonym="Latina" data-language-local-name="Λατινικά" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Fl%C3%A4ch" title="Fläch – Λουξεμβουργιανά" lang="lb" hreflang="lb" data-title="Fläch" data-language-autonym="Lëtzebuergesch" data-language-local-name="Λουξεμβουργιανά" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Oppervlak" title="Oppervlak – Λιμβουργιανά" lang="li" hreflang="li" data-title="Oppervlak" data-language-autonym="Limburgs" data-language-local-name="Λιμβουργιανά" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-lij mw-list-item"><a href="https://lij.wikipedia.org/wiki/Area" title="Area – Λιγουριανά" lang="lij" hreflang="lij" data-title="Area" data-language-autonym="Ligure" data-language-local-name="Λιγουριανά" class="interlanguage-link-target"><span>Ligure</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Area" title="Area – Λομβαρδικά" lang="lmo" hreflang="lmo" data-title="Area" data-language-autonym="Lombard" data-language-local-name="Λομβαρδικά" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-ln mw-list-item"><a href="https://ln.wikipedia.org/wiki/Etando" title="Etando – Λινγκάλα" lang="ln" hreflang="ln" data-title="Etando" data-language-autonym="Lingála" data-language-local-name="Λινγκάλα" class="interlanguage-link-target"><span>Lingála</span></a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%E0%BB%80%E0%BA%99%E0%BA%B7%E0%BB%89%E0%BA%AD%E0%BA%97%E0%BA%B5%E0%BB%88" title="ເນື້ອທີ່ – Λαοτινά" lang="lo" hreflang="lo" data-title="ເນື້ອທີ່" data-language-autonym="ລາວ" data-language-local-name="Λαοτινά" class="interlanguage-link-target"><span>ລາວ</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Plotas" title="Plotas – Λιθουανικά" lang="lt" hreflang="lt" data-title="Plotas" data-language-autonym="Lietuvių" data-language-local-name="Λιθουανικά" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Laukums" title="Laukums – Λετονικά" lang="lv" hreflang="lv" data-title="Laukums" data-language-autonym="Latviešu" data-language-local-name="Λετονικά" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mai mw-list-item"><a href="https://mai.wikipedia.org/wiki/%E0%A4%95%E0%A5%8D%E0%A4%B7%E0%A5%87%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%AB%E0%A4%B2" title="क्षेत्रफल – Μαϊτχίλι" lang="mai" hreflang="mai" data-title="क्षेत्रफल" data-language-autonym="मैथिली" data-language-local-name="Μαϊτχίλι" class="interlanguage-link-target"><span>मैथिली</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Velarana_(je%C3%B4metria)" title="Velarana (jeômetria) – Μαλγασικά" lang="mg" hreflang="mg" data-title="Velarana (jeômetria)" data-language-autonym="Malagasy" data-language-local-name="Μαλγασικά" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mhr mw-list-item"><a href="https://mhr.wikipedia.org/wiki/%D0%9A%D1%83%D0%BC%D0%B4%D1%8B%D0%BA" title="Кумдык – Eastern Mari" lang="mhr" hreflang="mhr" data-title="Кумдык" data-language-autonym="Олык марий" data-language-local-name="Eastern Mari" class="interlanguage-link-target"><span>Олык марий</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9F%D0%BB%D0%BE%D1%88%D1%82%D0%B8%D0%BD%D0%B0" title="Плоштина – Σλαβομακεδονικά" lang="mk" hreflang="mk" data-title="Плоштина" data-language-autonym="Македонски" data-language-local-name="Σλαβομακεδονικά" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B5%E0%B4%BF%E0%B4%B8%E0%B5%8D%E0%B4%A4%E0%B5%80%E0%B5%BC%E0%B4%A3%E0%B5%8D%E0%B4%A3%E0%B4%82" title="വിസ്തീർണ്ണം – Μαλαγιαλαμικά" lang="ml" hreflang="ml" data-title="വിസ്തീർണ്ണം" data-language-autonym="മലയാളം" data-language-local-name="Μαλαγιαλαμικά" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A2%D0%B0%D0%BB%D0%B1%D0%B0%D0%B9" title="Талбай – Μογγολικά" lang="mn" hreflang="mn" data-title="Талбай" data-language-autonym="Монгол" data-language-local-name="Μογγολικά" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-mni mw-list-item"><a href="https://mni.wikipedia.org/wiki/%EA%AF%84%EA%AF%A5%EA%AF%9B%EA%AF%86%EA%AF%A5%EA%AF%8E%EA%AF%95" title="ꯄꯥꯛꯆꯥꯎꯕ – Μανιπούρι" lang="mni" hreflang="mni" data-title="ꯄꯥꯛꯆꯥꯎꯕ" data-language-autonym="ꯃꯤꯇꯩ ꯂꯣꯟ" data-language-local-name="Μανιπούρι" class="interlanguage-link-target"><span>ꯃꯤꯇꯩ ꯂꯣꯟ</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%95%E0%A5%8D%E0%A4%B7%E0%A5%87%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%AB%E0%A4%B3" title="क्षेत्रफळ – Μαραθικά" lang="mr" hreflang="mr" data-title="क्षेत्रफळ" data-language-autonym="मराठी" data-language-local-name="Μαραθικά" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Luas" title="Luas – Μαλαισιανά" lang="ms" hreflang="ms" data-title="Luas" data-language-autonym="Bahasa Melayu" data-language-local-name="Μαλαισιανά" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/%C3%81ria" title="Ária – Μιραντεζικά" lang="mwl" hreflang="mwl" data-title="Ária" data-language-autonym="Mirandés" data-language-local-name="Μιραντεζικά" class="interlanguage-link-target"><span>Mirandés</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%A7%E1%80%9B%E1%80%AD%E1%80%9A%E1%80%AC" title="ဧရိယာ – Βιρμανικά" lang="my" hreflang="my" data-title="ဧရိယာ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Βιρμανικά" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-mzn mw-list-item"><a href="https://mzn.wikipedia.org/wiki/%DA%AF%D8%AA%DB%8C" title="گتی – Μαζαντεράνι" lang="mzn" hreflang="mzn" data-title="گتی" data-language-autonym="مازِرونی" data-language-local-name="Μαζαντεράνι" class="interlanguage-link-target"><span>مازِرونی</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Flach" title="Flach – Κάτω Γερμανικά" lang="nds" hreflang="nds" data-title="Flach" data-language-autonym="Plattdüütsch" data-language-local-name="Κάτω Γερμανικά" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-nds-nl mw-list-item"><a href="https://nds-nl.wikipedia.org/wiki/Oppervlakte" title="Oppervlakte – Κάτω Γερμανικά Ολλανδίας" lang="nds-NL" hreflang="nds-NL" data-title="Oppervlakte" data-language-autonym="Nedersaksies" data-language-local-name="Κάτω Γερμανικά Ολλανδίας" class="interlanguage-link-target"><span>Nedersaksies</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%95%E0%A5%8D%E0%A4%B7%E0%A5%87%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%AB%E0%A4%B2" title="क्षेत्रफल – Νεπαλικά" lang="ne" hreflang="ne" data-title="क्षेत्रफल" data-language-autonym="नेपाली" data-language-local-name="Νεπαλικά" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Oppervlakte" title="Oppervlakte – Ολλανδικά" lang="nl" hreflang="nl" data-title="Oppervlakte" data-language-autonym="Nederlands" data-language-local-name="Ολλανδικά" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Flatevidd" title="Flatevidd – Νορβηγικά Νινόρσκ" lang="nn" hreflang="nn" data-title="Flatevidd" data-language-autonym="Norsk nynorsk" data-language-local-name="Νορβηγικά Νινόρσκ" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Areal" title="Areal – Νορβηγικά Μποκμάλ" lang="nb" hreflang="nb" data-title="Areal" data-language-autonym="Norsk bokmål" data-language-local-name="Νορβηγικά Μποκμάλ" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Aira" title="Aira – Οξιτανικά" lang="oc" hreflang="oc" data-title="Aira" data-language-autonym="Occitan" data-language-local-name="Οξιτανικά" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-os mw-list-item"><a href="https://os.wikipedia.org/wiki/%D0%A4%C3%A6%D0%B7%D1%83%D0%B0%D1%82" title="Фæзуат – Οσετικά" lang="os" hreflang="os" data-title="Фæзуат" data-language-autonym="Ирон" data-language-local-name="Οσετικά" class="interlanguage-link-target"><span>Ирон</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%96%E0%A9%87%E0%A8%A4%E0%A8%B0%E0%A8%AB%E0%A8%B2" title="ਖੇਤਰਫਲ – Παντζαπικά" lang="pa" hreflang="pa" data-title="ਖੇਤਰਫਲ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Παντζαπικά" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pfl mw-list-item"><a href="https://pfl.wikipedia.org/wiki/Fl%C3%A4che" title="Fläche – Palatine German" lang="pfl" hreflang="pfl" data-title="Fläche" data-language-autonym="Pälzisch" data-language-local-name="Palatine German" class="interlanguage-link-target"><span>Pälzisch</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Pole_powierzchni" title="Pole powierzchni – Πολωνικά" lang="pl" hreflang="pl" data-title="Pole powierzchni" data-language-autonym="Polski" data-language-local-name="Πολωνικά" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%B1%D9%82%D8%A8%DB%81" title="رقبہ – Western Punjabi" lang="pnb" hreflang="pnb" data-title="رقبہ" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/%C3%81rea" title="Área – Πορτογαλικά" lang="pt" hreflang="pt" data-title="Área" data-language-autonym="Português" data-language-local-name="Πορτογαλικά" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Hallka_k%27iti_k%27anchar" title="Hallka k'iti k'anchar – Κέτσουα" lang="qu" hreflang="qu" data-title="Hallka k'iti k'anchar" data-language-autonym="Runa Simi" data-language-local-name="Κέτσουα" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Arie" title="Arie – Ρουμανικά" lang="ro" hreflang="ro" data-title="Arie" data-language-autonym="Română" data-language-local-name="Ρουμανικά" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9F%D0%BB%D0%BE%D1%89%D0%B0%D0%B4%D1%8C" title="Площадь – Ρωσικά" lang="ru" hreflang="ru" data-title="Площадь" data-language-autonym="Русский" data-language-local-name="Ρωσικά" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sa mw-list-item"><a href="https://sa.wikipedia.org/wiki/%E0%A4%95%E0%A5%8D%E0%A4%B7%E0%A5%87%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%AB%E0%A4%B2%E0%A4%AE%E0%A5%8D" title="क्षेत्रफलम् – Σανσκριτικά" lang="sa" hreflang="sa" data-title="क्षेत्रफलम्" data-language-autonym="संस्कृतम्" data-language-local-name="Σανσκριτικά" class="interlanguage-link-target"><span>संस्कृतम्</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%98%D1%8D%D0%BD" title="Иэн – Σαχά" lang="sah" hreflang="sah" data-title="Иэн" data-language-autonym="Саха тыла" data-language-local-name="Σαχά" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/%C3%80ria_(supirfici)" title="Ària (supirfici) – Σικελικά" lang="scn" hreflang="scn" data-title="Ària (supirfici)" data-language-autonym="Sicilianu" data-language-local-name="Σικελικά" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Area" title="Area – Σκωτικά" lang="sco" hreflang="sco" data-title="Area" data-language-autonym="Scots" data-language-local-name="Σκωτικά" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D8%A7%D9%8A%D8%B1%D8%A7%D8%B6%D9%8A" title="ايراضي – Σίντι" lang="sd" hreflang="sd" data-title="ايراضي" data-language-autonym="سنڌي" data-language-local-name="Σίντι" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Povr%C5%A1ina" title="Površina – Σερβοκροατικά" lang="sh" hreflang="sh" data-title="Površina" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Σερβοκροατικά" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Area" title="Area – Simple English" lang="en-simple" hreflang="en-simple" data-title="Area" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Plocha_(%C3%BAtvar)" title="Plocha (útvar) – Σλοβακικά" lang="sk" hreflang="sk" data-title="Plocha (útvar)" data-language-autonym="Slovenčina" data-language-local-name="Σλοβακικά" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Povr%C5%A1ina" title="Površina – Σλοβενικά" lang="sl" hreflang="sl" data-title="Površina" data-language-autonym="Slovenščina" data-language-local-name="Σλοβενικά" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Nharaunda" title="Nharaunda – Σόνα" lang="sn" hreflang="sn" data-title="Nharaunda" data-language-autonym="ChiShona" data-language-local-name="Σόνα" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Bed" title="Bed – Σομαλικά" lang="so" hreflang="so" data-title="Bed" data-language-autonym="Soomaaliga" data-language-local-name="Σομαλικά" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Sip%C3%ABrfaqja" title="Sipërfaqja – Αλβανικά" lang="sq" hreflang="sq" data-title="Sipërfaqja" data-language-autonym="Shqip" data-language-local-name="Αλβανικά" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9F%D0%BE%D0%B2%D1%80%D1%88%D0%B8%D0%BD%D0%B0" title="Површина – Σερβικά" lang="sr" hreflang="sr" data-title="Површина" data-language-autonym="Српски / srpski" data-language-local-name="Σερβικά" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Ar%C3%A9a" title="Aréa – Σουνδανικά" lang="su" hreflang="su" data-title="Aréa" data-language-autonym="Sunda" data-language-local-name="Σουνδανικά" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Area" title="Area – Σουηδικά" lang="sv" hreflang="sv" data-title="Area" data-language-autonym="Svenska" data-language-local-name="Σουηδικά" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Eneo" title="Eneo – Σουαχίλι" lang="sw" hreflang="sw" data-title="Eneo" data-language-autonym="Kiswahili" data-language-local-name="Σουαχίλι" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-szl mw-list-item"><a href="https://szl.wikipedia.org/wiki/Plac_rozlygowa%C5%84o" title="Plac rozlygowańo – Σιλεσικά" lang="szl" hreflang="szl" data-title="Plac rozlygowańo" data-language-autonym="Ślůnski" data-language-local-name="Σιλεσικά" class="interlanguage-link-target"><span>Ślůnski</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AA%E0%AE%B0%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AE%B3%E0%AE%B5%E0%AF%81" title="பரப்பளவு – Ταμιλικά" lang="ta" hreflang="ta" data-title="பரப்பளவு" data-language-autonym="தமிழ்" data-language-local-name="Ταμιλικά" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%B5%E0%B0%BF%E0%B0%B8%E0%B1%8D%E0%B0%A4%E0%B1%80%E0%B0%B0%E0%B1%8D%E0%B0%A3%E0%B0%82" title="విస్తీర్ణం – Τελούγκου" lang="te" hreflang="te" data-title="విస్తీర్ణం" data-language-autonym="తెలుగు" data-language-local-name="Τελούγκου" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%9C%D0%B0%D1%81%D0%BE%D2%B3%D0%B0%D1%82" title="Масоҳат – Τατζικικά" lang="tg" hreflang="tg" data-title="Масоҳат" data-language-autonym="Тоҷикӣ" data-language-local-name="Τατζικικά" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%9E%E0%B8%B7%E0%B9%89%E0%B8%99%E0%B8%97%E0%B8%B5%E0%B9%88" title="พื้นที่ – Ταϊλανδικά" lang="th" hreflang="th" data-title="พื้นที่" data-language-autonym="ไทย" data-language-local-name="Ταϊλανδικά" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-ti mw-list-item"><a href="https://ti.wikipedia.org/wiki/%E1%8C%BD%E1%8D%8D%E1%88%93%E1%89%B5_%E1%88%98%E1%88%AC%E1%89%B5" title="ጽፍሓት መሬት – Τιγκρινικά" lang="ti" hreflang="ti" data-title="ጽፍሓት መሬት" data-language-autonym="ትግርኛ" data-language-local-name="Τιγκρινικά" class="interlanguage-link-target"><span>ትግርኛ</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Sukat" title="Sukat – Τάγκαλογκ" lang="tl" hreflang="tl" data-title="Sukat" data-language-autonym="Tagalog" data-language-local-name="Τάγκαλογκ" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Alan" title="Alan – Τουρκικά" lang="tr" hreflang="tr" data-title="Alan" data-language-autonym="Türkçe" data-language-local-name="Τουρκικά" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/M%C3%A4ydan" title="Mäydan – Ταταρικά" lang="tt" hreflang="tt" data-title="Mäydan" data-language-autonym="Татарча / tatarça" data-language-local-name="Ταταρικά" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9F%D0%BB%D0%BE%D1%89%D0%B0" title="Площа – Ουκρανικά" lang="uk" hreflang="uk" data-title="Площа" data-language-autonym="Українська" data-language-local-name="Ουκρανικά" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%B1%D9%82%D8%A8%DB%81" title="رقبہ – Ούρντου" lang="ur" hreflang="ur" data-title="رقبہ" data-language-autonym="اردو" data-language-local-name="Ούρντου" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Yuza" title="Yuza – Ουζμπεκικά" lang="uz" hreflang="uz" data-title="Yuza" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Ουζμπεκικά" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Di%E1%BB%87n_t%C3%ADch" title="Diện tích – Βιετναμικά" lang="vi" hreflang="vi" data-title="Diện tích" data-language-autonym="Tiếng Việt" data-language-local-name="Βιετναμικά" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-vls mw-list-item"><a href="https://vls.wikipedia.org/wiki/Ippervlak" title="Ippervlak – West Flemish" lang="vls" hreflang="vls" data-title="Ippervlak" data-language-autonym="West-Vlams" data-language-local-name="West Flemish" class="interlanguage-link-target"><span>West-Vlams</span></a></li><li class="interlanguage-link interwiki-wa mw-list-item"><a href="https://wa.wikipedia.org/wiki/Sitind%C3%AAye" title="Sitindêye – Βαλλωνικά" lang="wa" hreflang="wa" data-title="Sitindêye" data-language-autonym="Walon" data-language-local-name="Βαλλωνικά" class="interlanguage-link-target"><span>Walon</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Kahaluag" title="Kahaluag – Γουάραϊ" lang="war" hreflang="war" data-title="Kahaluag" data-language-autonym="Winaray" data-language-local-name="Γουάραϊ" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wo mw-list-item"><a href="https://wo.wikipedia.org/wiki/Yaatuwaay" title="Yaatuwaay – Γουόλοφ" lang="wo" hreflang="wo" data-title="Yaatuwaay" data-language-autonym="Wolof" data-language-local-name="Γουόλοφ" class="interlanguage-link-target"><span>Wolof</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E9%9D%A2%E7%A7%AF" title="面积 – Κινεζικά Γου" lang="wuu" hreflang="wuu" data-title="面积" data-language-autonym="吴语" data-language-local-name="Κινεζικά Γου" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%A4%E1%83%90%E1%83%A0%E1%83%97%E1%83%9D%E1%83%91%E1%83%98" title="ფართობი – Mingrelian" lang="xmf" hreflang="xmf" data-title="ფართობი" data-language-autonym="მარგალური" data-language-local-name="Mingrelian" class="interlanguage-link-target"><span>მარგალური</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A9%D7%98%D7%97" title="שטח – Γίντις" lang="yi" hreflang="yi" data-title="שטח" data-language-autonym="ייִדיש" data-language-local-name="Γίντις" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-yo mw-list-item"><a href="https://yo.wikipedia.org/wiki/%C3%80%C3%A0l%C3%A0" title="Ààlà – Γιορούμπα" lang="yo" hreflang="yo" data-title="Ààlà" data-language-autonym="Yorùbá" data-language-local-name="Γιορούμπα" class="interlanguage-link-target"><span>Yorùbá</span></a></li><li class="interlanguage-link interwiki-zea mw-list-item"><a href="https://zea.wikipedia.org/wiki/Oppervlak" title="Oppervlak – Zeelandic" lang="zea" hreflang="zea" data-title="Oppervlak" data-language-autonym="Zeêuws" data-language-local-name="Zeelandic" class="interlanguage-link-target"><span>Zeêuws</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E9%9D%A2%E7%A7%AF" title="面积 – Κινεζικά" lang="zh" hreflang="zh" data-title="面积" data-language-autonym="中文" data-language-local-name="Κινεζικά" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Bi%C4%81n-chek" title="Biān-chek – Minnan" lang="nan" hreflang="nan" data-title="Biān-chek" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E9%9D%A2%E7%A9%8D" title="面積 – Καντονέζικα" lang="yue" hreflang="yue" data-title="面積" data-language-autonym="粵語" data-language-local-name="Καντονέζικα" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q11500#sitelinks-wikipedia" title="Επεξεργασία διαγλωσσικών συνδέσεων" class="wbc-editpage">Επεξεργασία συνδέσμων</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Ονοματοχώροι"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD" title="Προβολή της σελίδας περιεχομένου [c]" accesskey="c"><span>Λήμμα</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/%CE%A3%CF%85%CE%B6%CE%AE%CF%84%CE%B7%CF%83%CE%B7:%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD" rel="discussion" title="Συζήτηση για τη σελίδα περιεχομένου [t]" accesskey="t"><span>Συζήτηση</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Αλλαγή παραλλαγής γλώσσας" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Ελληνικά</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div 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class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Εργαλεία</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">μετακίνηση στην πλαϊνή μπάρα</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">απόκρυψη</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Περισσότερες επιλογές" > <div class="vector-menu-heading"> Ενέργειες </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD"><span>Ανάγνωση</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&veaction=edit" title="Επεξεργασία αυτής της σελίδας [v]" accesskey="v"><span>Επεξεργασία</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&action=edit" title="Επεξεργασία του πηγαίου κώδικα της σελίδας [e]" accesskey="e"><span>Επεξεργασία κώδικα</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&action=history"><span>Προβολή ιστορικού</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Γενικά </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/%CE%95%CE%B9%CE%B4%CE%B9%CE%BA%CF%8C:%CE%A4%CE%B9%CE%A3%CF%85%CE%BD%CE%B4%CE%AD%CE%B5%CE%B9%CE%95%CE%B4%CF%8E/%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD" title="Κατάλογος όλων των σελίδων wiki που έχουν συνδέσμους προς εδώ [j]" accesskey="j"><span>Συνδέσεις προς εδώ</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/%CE%95%CE%B9%CE%B4%CE%B9%CE%BA%CF%8C:%CE%A3%CF%85%CE%BD%CE%B4%CE%B5%CE%B4%CE%B5%CE%BC%CE%AD%CE%BD%CE%B5%CF%82%CE%A0%CF%81%CF%8C%CF%83%CF%86%CE%B1%CF%84%CE%B5%CF%82%CE%91%CE%BB%CE%BB%CE%B1%CE%B3%CE%AD%CF%82/%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD" rel="nofollow" title="Πρόσφατες αλλαγές σε σελίδες που παραπέμπουν οι σύνδεσμοι αυτής της σελίδας [k]" accesskey="k"><span>Σχετικές αλλαγές</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&oldid=11029762" title="Μόνιμος σύνδεσμος προς αυτήν την αναθεώρηση αυτής της σελίδας"><span>Σταθερός σύνδεσμος</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&action=info" title="Περισσότερες πληροφορίες σχετικά με αυτήν τη σελίδα"><span>Πληροφορίες σελίδας</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=%CE%95%CE%B9%CE%B4%CE%B9%CE%BA%CF%8C:%CE%A0%CE%B1%CF%81%CE%B1%CF%80%CE%BF%CE%BC%CF%80%CE%AE%CE%91%CF%85%CF%84%CE%AE%CE%A4%CE%B7%CE%A3%CE%B5%CE%BB%CE%AF%CE%B4%CE%B1&page=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&id=11029762&wpFormIdentifier=titleform" title="Πληροφορίες για το πώς να δημιουργήσετε παραπομπή αυτής της σελίδας"><span>Παραπομπή</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=%CE%95%CE%B9%CE%B4%CE%B9%CE%BA%CF%8C:UrlShortener&url=https%3A%2F%2Fel.wikipedia.org%2Fwiki%2F%25CE%2595%25CE%25BC%25CE%25B2%25CE%25B1%25CE%25B4%25CF%258C%25CE%25BD"><span>Λάβετε συντομευμένη διεύθυνση URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=%CE%95%CE%B9%CE%B4%CE%B9%CE%BA%CF%8C:QrCode&url=https%3A%2F%2Fel.wikipedia.org%2Fwiki%2F%25CE%2595%25CE%25BC%25CE%25B2%25CE%25B1%25CE%25B4%25CF%258C%25CE%25BD"><span>Λήψη κωδικού QR</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Εκτύπωση/εξαγωγή </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=%CE%95%CE%B9%CE%B4%CE%B9%CE%BA%CF%8C:%CE%A3%CF%85%CE%BB%CE%BB%CE%BF%CE%B3%CE%AE&bookcmd=book_creator&referer=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD"><span>Δημιουργία βιβλίου</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=%CE%95%CE%B9%CE%B4%CE%B9%CE%BA%CF%8C:DownloadAsPdf&page=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&action=show-download-screen"><span>Κατέβασμα ως PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&printable=yes" title="Εκτυπώσιμη έκδοση αυτής της σελίδας [p]" accesskey="p"><span>Εκτυπώσιμη έκδοση</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> Σε άλλα εγχειρήματα </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Area" hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q11500" title="Σύνδεσμος προς το συνδεδεμένο αντικείμενο δεδομένων [g]" accesskey="g"><span>Αντικείμενο Wikidata</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Εργαλεία σελίδων"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Εμφάνιση"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Εμφάνιση</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">μετακίνηση στην πλαϊνή μπάρα</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">απόκρυψη</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Από τη Βικιπαίδεια, την ελεύθερη εγκυκλοπαίδεια</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="el" dir="ltr"><p><b>Εμβαδόν</b> ή <i>έκταση</i> είναι το μέγεθος <a href="/wiki/%CE%9C%CE%AD%CF%84%CF%81%CE%B7%CF%83%CE%B7" title="Μέτρηση">μέτρησης</a> των <a href="/w/index.php?title=%CE%95%CF%80%CE%B9%CF%86%CE%AC%CE%BD%CE%B5%CE%B9%CE%B1_(%CE%B3%CE%B5%CF%89%CE%BC%CE%B5%CF%84%CF%81%CE%AF%CE%B1)&action=edit&redlink=1" class="new" title="Επιφάνεια (γεωμετρία) (δεν έχει γραφτεί ακόμα)">επιφανειών</a>.<sup id="cite_ref-Tav_1-0" class="reference"><a href="#cite_note-Tav-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup class="reference" style="white-space:nowrap;">:232-245</sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup class="reference" style="white-space:nowrap;">:91-140</sup> Συμβολίζεται συνήθως με το γράμμα <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af444c1459d0e1a3e34afa76cd4d026aabeba198" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.176ex;" alt="{\displaystyle {\rm {E}}}" /></span> ή το γράμμα <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {A}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {A}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d483866242c3b3266289fb4d3bdd0b3b947863e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle {\rm {A}}}" /></span> (το τελευταίο χρησιμοποιείται συνήθως στην επιφάνεια <a href="/w/index.php?title=%CE%94%CE%B9%CE%B1%CF%84%CE%BF%CE%BC%CE%AE&action=edit&redlink=1" class="new" title="Διατομή (δεν έχει γραφτεί ακόμα)">διατομής</a>). Η μονάδα μέτρησης στο <a href="/wiki/%CE%94%CE%B9%CE%B5%CE%B8%CE%BD%CE%AD%CF%82_%CF%83%CF%8D%CF%83%CF%84%CE%B7%CE%BC%CE%B1_%CE%BC%CE%BF%CE%BD%CE%AC%CE%B4%CF%89%CE%BD" title="Διεθνές σύστημα μονάδων">διεθνές σύστημα</a> είναι το <a href="/wiki/%CE%A4%CE%B5%CF%84%CF%81%CE%B1%CE%B3%CF%89%CE%BD%CE%B9%CE%BA%CF%8C_%CE%BC%CE%AD%CF%84%CF%81%CE%BF" title="Τετραγωνικό μέτρο">1m²</a>. Το εμβαδόν θεωρείται ένα βασικό μέγεθος των δισδιάστατων σχημάτων, όπως τα τετράγωνα και οι κύκλοι, τα οποία δεν έχουν <a href="/wiki/%CE%8C%CE%B3%CE%BA%CE%BF%CF%82" title="Όγκος">όγκο</a>. Όταν αναφέρεται σε τρισδιάστατα σχήματα συνήθως εννοείται το εμβαδόν της εξωτερικής επιφάνειας του σώματος. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Λίστα_τύπων_υπολογισμού_εμβαδού_διαφόρων_σχημάτων"><span id=".CE.9B.CE.AF.CF.83.CF.84.CE.B1_.CF.84.CF.8D.CF.80.CF.89.CE.BD_.CF.85.CF.80.CE.BF.CE.BB.CE.BF.CE.B3.CE.B9.CF.83.CE.BC.CE.BF.CF.8D_.CE.B5.CE.BC.CE.B2.CE.B1.CE.B4.CE.BF.CF.8D_.CE.B4.CE.B9.CE.B1.CF.86.CF.8C.CF.81.CF.89.CE.BD_.CF.83.CF.87.CE.B7.CE.BC.CE.AC.CF.84.CF.89.CE.BD"></span>Λίστα τύπων υπολογισμού εμβαδού διαφόρων σχημάτων</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&veaction=edit&section=1" title="Επεξεργασία ενότητας: Λίστα τύπων υπολογισμού εμβαδού διαφόρων σχημάτων" class="mw-editsection-visualeditor"><span>Επεξεργασία</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&action=edit&section=1" title="Επεξεργαστείτε τον πηγαίο κώδικα της ενότητας: Λίστα τύπων υπολογισμού εμβαδού διαφόρων σχημάτων"><span>επεξεργασία κώδικα</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Παρακάτω δίνονται οι τύποι για τον υπολογισμό των πιο κοινών <a href="/wiki/%CE%93%CE%B5%CF%89%CE%BC%CE%B5%CF%84%CF%81%CE%B9%CE%BA%CF%8C_%CF%83%CF%87%CE%AE%CE%BC%CE%B1" title="Γεωμετρικό σχήμα">γεωμετρικών σχημάτων</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Τρίγωνο"><span id=".CE.A4.CF.81.CE.AF.CE.B3.CF.89.CE.BD.CE.BF"></span>Τρίγωνο</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&veaction=edit&section=2" title="Επεξεργασία ενότητας: Τρίγωνο" class="mw-editsection-visualeditor"><span>Επεξεργασία</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&action=edit&section=2" title="Επεξεργαστείτε τον πηγαίο κώδικα της ενότητας: Τρίγωνο"><span>επεξεργασία κώδικα</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Σε ένα τρίγωνο <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {AB\Gamma }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> <mi mathvariant="normal">B</mi> <mi mathvariant="normal">Γ</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {AB\Gamma }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ebe8dc4aaf786375cefdcb296275bf8322d502f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.841ex; height:2.176ex;" alt="{\displaystyle {\rm {AB\Gamma }}}" /></span> ισχύουν οι εξής τύποι για το εμβαδόν του </p> <ul><li>Αν <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \upsilon _{\rm {A}},\upsilon _{\rm {B}},\upsilon _{\rm {\Gamma }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>υ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> <mo>,</mo> <msub> <mi>υ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <mo>,</mo> <msub> <mi>υ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \upsilon _{\rm {A}},\upsilon _{\rm {B}},\upsilon _{\rm {\Gamma }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/55536d1bf64252cf120cc61354741554595a8dbd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.954ex; height:2.009ex;" alt="{\displaystyle \upsilon _{\rm {A}},\upsilon _{\rm {B}},\upsilon _{\rm {\Gamma }}}" /></span> είναι τα <a href="/wiki/%CE%8E%CF%88%CE%BF%CF%82_%CF%84%CF%81%CE%B9%CE%B3%CF%8E%CE%BD%CE%BF%CF%85" title="Ύψος τριγώνου">ύψη</a> του τριγώνου, τότε<sup id="cite_ref-T57_3-0" class="reference"><a href="#cite_note-T57-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Σελίδα: 459">: 459 </span></sup></li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}={\tfrac {1}{2}}\cdot \alpha \cdot \upsilon _{\rm {A}}={\tfrac {1}{2}}\cdot \beta \cdot \upsilon _{\rm {B}}={\tfrac {1}{2}}\cdot \gamma \cdot \upsilon _{\rm {\Gamma }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <mo>⋅</mo> <mi>α</mi> <mo>⋅</mo> <msub> <mi>υ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <mo>⋅</mo> <mi>β</mi> <mo>⋅</mo> <msub> <mi>υ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <mo>⋅</mo> <mi>γ</mi> <mo>⋅</mo> <msub> <mi>υ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}={\tfrac {1}{2}}\cdot \alpha \cdot \upsilon _{\rm {A}}={\tfrac {1}{2}}\cdot \beta \cdot \upsilon _{\rm {B}}={\tfrac {1}{2}}\cdot \gamma \cdot \upsilon _{\rm {\Gamma }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fea8dacc712dc239d2dc7bd37413149717d46eba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:37.895ex; height:3.509ex;" alt="{\displaystyle {\rm {E}}={\tfrac {1}{2}}\cdot \alpha \cdot \upsilon _{\rm {A}}={\tfrac {1}{2}}\cdot \beta \cdot \upsilon _{\rm {B}}={\tfrac {1}{2}}\cdot \gamma \cdot \upsilon _{\rm {\Gamma }}}" /></span>.</dd></dl></dd></dl> <ul><li>(<b><a href="/wiki/%CE%A4%CF%8D%CF%80%CE%BF%CF%82_%CF%84%CE%BF%CF%85_%CE%89%CF%81%CF%89%CE%BD%CE%B1" title="Τύπος του Ήρωνα">Τύπος του Ήρωνα</a></b>) Σε ένα τρίγωνο με μήκη πλευρών <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha ,\beta ,\gamma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mo>,</mo> <mi>β</mi> <mo>,</mo> <mi>γ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha ,\beta ,\gamma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/301cc1b37ba8f0fb0c9bedee5efa5e0b5bc9e791" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.15ex; height:2.676ex;" alt="{\displaystyle \alpha ,\beta ,\gamma }" /></span>, έχουμε ότι<sup id="cite_ref-T57_3-1" class="reference"><a href="#cite_note-T57-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Σελίδα: 461">: 461 </span></sup></li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}={\sqrt {\tau \cdot (\tau -\alpha )\cdot (\tau -\beta )\cdot (\tau -\gamma )}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>τ</mi> <mo>⋅</mo> <mo stretchy="false">(</mo> <mi>τ</mi> <mo>−</mo> <mi>α</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mo stretchy="false">(</mo> <mi>τ</mi> <mo>−</mo> <mi>β</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mo stretchy="false">(</mo> <mi>τ</mi> <mo>−</mo> <mi>γ</mi> <mo stretchy="false">)</mo> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}={\sqrt {\tau \cdot (\tau -\alpha )\cdot (\tau -\beta )\cdot (\tau -\gamma )}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/458cec3c3e33bde75180d2582ebbe9b9285f42bb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:34.881ex; height:4.843ex;" alt="{\displaystyle {\rm {E}}={\sqrt {\tau \cdot (\tau -\alpha )\cdot (\tau -\beta )\cdot (\tau -\gamma )}}}" /></span>,</dd></dl></dd> <dd>όπου <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>τ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38a7dcde9730ef0853809fefc18d88771f95206c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.202ex; height:1.676ex;" alt="{\displaystyle \tau }" /></span> είναι η <a href="/wiki/%CE%97%CE%BC%CE%B9%CF%80%CE%B5%CF%81%CE%AF%CE%BC%CE%B5%CF%84%CF%81%CE%BF%CF%82" title="Ημιπερίμετρος">ημιπερίμετρος</a>.</dd></dl> <ul><li>Σε ένα τρίγωνο <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {AB\Gamma }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> <mi mathvariant="normal">B</mi> <mi mathvariant="normal">Γ</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {AB\Gamma }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ebe8dc4aaf786375cefdcb296275bf8322d502f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.841ex; height:2.176ex;" alt="{\displaystyle {\rm {AB\Gamma }}}" /></span>, ισχύει ότι</li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}={\tfrac {1}{2}}\beta \gamma \sin {\rm {A={\tfrac {1}{2}}\alpha \gamma \sin {\rm {B={\tfrac {1}{2}}\alpha \beta \sin {\rm {\Gamma }}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <mi>β</mi> <mi>γ</mi> <mi>sin</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <mi>α</mi> <mi>γ</mi> <mi>sin</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <mi>α</mi> <mi>β</mi> <mi>sin</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}={\tfrac {1}{2}}\beta \gamma \sin {\rm {A={\tfrac {1}{2}}\alpha \gamma \sin {\rm {B={\tfrac {1}{2}}\alpha \beta \sin {\rm {\Gamma }}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6290ca49b97dabc240baac5ed6c26d649de479b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:39.747ex; height:3.509ex;" alt="{\displaystyle {\rm {E}}={\tfrac {1}{2}}\beta \gamma \sin {\rm {A={\tfrac {1}{2}}\alpha \gamma \sin {\rm {B={\tfrac {1}{2}}\alpha \beta \sin {\rm {\Gamma }}}}}}}" /></span>,</dd></dl></dd> <dd>όπου <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {\sin A,\sin B,\sin \Gamma }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi>sin</mi> <mo>⁡</mo> <mi mathvariant="normal">A</mi> <mo>,</mo> <mi>sin</mi> <mo>⁡</mo> <mi mathvariant="normal">B</mi> <mo>,</mo> <mi>sin</mi> <mo>⁡</mo> <mi mathvariant="normal">Γ</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {\sin A,\sin B,\sin \Gamma }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8d51ed92d42bc0bd488b89e4f87ecee9680dd492" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:16.637ex; height:2.509ex;" alt="{\displaystyle {\rm {\sin A,\sin B,\sin \Gamma }}}" /></span> τα ημίτονα των τριών γωνιών του.</dd></dl> <ul><li>Αν <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>τ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38a7dcde9730ef0853809fefc18d88771f95206c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.202ex; height:1.676ex;" alt="{\displaystyle \tau }" /></span> είναι η <a href="/wiki/%CE%97%CE%BC%CE%B9%CF%80%CE%B5%CF%81%CE%AF%CE%BC%CE%B5%CF%84%CF%81%CE%BF%CF%82" title="Ημιπερίμετρος">ημιπερίμετρος</a> και <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }" /></span> η ακτίνα του <a href="/wiki/%CE%95%CE%B3%CE%B3%CE%B5%CE%B3%CF%81%CE%B1%CE%BC%CE%BC%CE%AD%CE%BD%CE%BF%CF%82_%CE%BA%CF%8D%CE%BA%CE%BB%CE%BF%CF%82_%CF%84%CF%81%CE%B9%CE%B3%CF%8E%CE%BD%CE%BF%CF%85" class="mw-redirect" title="Εγγεγραμμένος κύκλος τριγώνου">εγγεγραμμένου κύκλου</a> του τριγώνου, τότε<sup id="cite_ref-Tav_1-1" class="reference"><a href="#cite_note-Tav-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Σελίδα: 238">: 238 </span></sup><sup id="cite_ref-T57_3-2" class="reference"><a href="#cite_note-T57-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Σελίδα: 462">: 462 </span></sup></li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}=\tau \cdot \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mo>=</mo> <mi>τ</mi> <mo>⋅</mo> <mi>ρ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}=\tau \cdot \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b95ea4355b2aa644c013f771ebbc237759a0fd45" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.764ex; height:2.676ex;" alt="{\displaystyle {\rm {E}}=\tau \cdot \rho }" /></span>.</dd></dl></dd></dl> <ul><li>Αν <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>τ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38a7dcde9730ef0853809fefc18d88771f95206c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.202ex; height:1.676ex;" alt="{\displaystyle \tau }" /></span> είναι η <a href="/wiki/%CE%97%CE%BC%CE%B9%CF%80%CE%B5%CF%81%CE%AF%CE%BC%CE%B5%CF%84%CF%81%CE%BF%CF%82" title="Ημιπερίμετρος">ημιπερίμετρος</a> και <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho _{\rm {A}},\rho _{\rm {B}},\rho _{\rm {\Gamma }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> <mo>,</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <mo>,</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho _{\rm {A}},\rho _{\rm {B}},\rho _{\rm {\Gamma }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d7bcd3a581905c6502a38e6928379f5b78e0fb3d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.794ex; height:2.176ex;" alt="{\displaystyle \rho _{\rm {A}},\rho _{\rm {B}},\rho _{\rm {\Gamma }}}" /></span> οι ακτίνες των <a href="/wiki/%CE%A0%CE%B1%CF%81%CE%B5%CE%B3%CE%B3%CE%B5%CE%B3%CF%81%CE%B1%CE%BC%CE%BC%CE%AD%CE%BD%CE%BF%CE%B9_%CE%BA%CF%8D%CE%BA%CE%BB%CE%BF%CE%B9_%CF%84%CF%81%CE%B9%CE%B3%CF%8E%CE%BD%CE%BF%CF%85" class="mw-redirect" title="Παρεγγεγραμμένοι κύκλοι τριγώνου">παρεγγεγραμμένων κύκλων</a> του τριγώνου, τότε<sup id="cite_ref-Tav_1-2" class="reference"><a href="#cite_note-Tav-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Σελίδα: 238">: 238 </span></sup><sup id="cite_ref-T57_3-3" class="reference"><a href="#cite_note-T57-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Σελίδα: 462">: 462 </span></sup></li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}=(\tau -\alpha )\cdot \rho _{\rm {A}}=(\tau -\beta )\cdot \rho _{\rm {B}}=(\tau -\gamma )\cdot \rho _{\rm {\Gamma }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mo>=</mo> <mo stretchy="false">(</mo> <mi>τ</mi> <mo>−</mo> <mi>α</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <mi>τ</mi> <mo>−</mo> <mi>β</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <mi>τ</mi> <mo>−</mo> <mi>γ</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}=(\tau -\alpha )\cdot \rho _{\rm {A}}=(\tau -\beta )\cdot \rho _{\rm {B}}=(\tau -\gamma )\cdot \rho _{\rm {\Gamma }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/350121d1546bec1bd0fc5f240b54b4776c25ad33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:45.278ex; height:2.843ex;" alt="{\displaystyle {\rm {E}}=(\tau -\alpha )\cdot \rho _{\rm {A}}=(\tau -\beta )\cdot \rho _{\rm {B}}=(\tau -\gamma )\cdot \rho _{\rm {\Gamma }}}" /></span>.</dd></dl></dd></dl> <ul><li>Αν <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>τ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38a7dcde9730ef0853809fefc18d88771f95206c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.202ex; height:1.676ex;" alt="{\displaystyle \tau }" /></span> είναι η <a href="/wiki/%CE%97%CE%BC%CE%B9%CF%80%CE%B5%CF%81%CE%AF%CE%BC%CE%B5%CF%84%CF%81%CE%BF%CF%82" title="Ημιπερίμετρος">ημιπερίμετρος</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }" /></span> η ακτίνα του <a href="/wiki/%CE%95%CE%B3%CE%B3%CE%B5%CE%B3%CF%81%CE%B1%CE%BC%CE%BC%CE%AD%CE%BD%CE%BF%CF%82_%CE%BA%CF%8D%CE%BA%CE%BB%CE%BF%CF%82_%CF%84%CF%81%CE%B9%CE%B3%CF%8E%CE%BD%CE%BF%CF%85" class="mw-redirect" title="Εγγεγραμμένος κύκλος τριγώνου">εγγεγραμμένος κύκλος</a> και <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho _{\rm {A}},\rho _{\rm {B}},\rho _{\rm {\Gamma }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> <mo>,</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <mo>,</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho _{\rm {A}},\rho _{\rm {B}},\rho _{\rm {\Gamma }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d7bcd3a581905c6502a38e6928379f5b78e0fb3d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.794ex; height:2.176ex;" alt="{\displaystyle \rho _{\rm {A}},\rho _{\rm {B}},\rho _{\rm {\Gamma }}}" /></span> οι ακτίνες των <a href="/wiki/%CE%A0%CE%B1%CF%81%CE%B5%CE%B3%CE%B3%CE%B5%CE%B3%CF%81%CE%B1%CE%BC%CE%BC%CE%AD%CE%BD%CE%BF%CE%B9_%CE%BA%CF%8D%CE%BA%CE%BB%CE%BF%CE%B9_%CF%84%CF%81%CE%B9%CE%B3%CF%8E%CE%BD%CE%BF%CF%85" class="mw-redirect" title="Παρεγγεγραμμένοι κύκλοι τριγώνου">παρεγγεγραμμένων κύκλων</a> του τριγώνου, τότε<sup id="cite_ref-Tav_1-3" class="reference"><a href="#cite_note-Tav-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Σελίδα: 238">: 238 </span></sup></li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}={\sqrt {\rho \cdot \rho _{\rm {A}}\cdot \rho _{\rm {B}}\cdot \rho _{\rm {\Gamma }}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>ρ</mi> <mo>⋅</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> <mo>⋅</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <mo>⋅</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> </mrow> </mrow> </msub> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}={\sqrt {\rho \cdot \rho _{\rm {A}}\cdot \rho _{\rm {B}}\cdot \rho _{\rm {\Gamma }}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e34451ac2240da98aa50e07d01e5cce70a6d73f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:20.582ex; height:3.009ex;" alt="{\displaystyle {\rm {E}}={\sqrt {\rho \cdot \rho _{\rm {A}}\cdot \rho _{\rm {B}}\cdot \rho _{\rm {\Gamma }}}}}" /></span>.</dd></dl></dd></dl> <ul><li>Αν <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}" /></span> η ακτίνα του <a href="/wiki/%CE%A0%CE%B5%CF%81%CE%B9%CE%B3%CE%B5%CE%B3%CF%81%CE%B1%CE%BC%CE%BC%CE%AD%CE%BD%CE%BF%CF%82_%CE%BA%CF%8D%CE%BA%CE%BB%CE%BF%CF%82_%CF%84%CF%81%CE%B9%CE%B3%CF%8E%CE%BD%CE%BF%CF%85" title="Περιγεγραμμένος κύκλος τριγώνου">περιγεγραμμένου κύκλου</a> του τριγώνου, τότε<sup id="cite_ref-Tav_1-4" class="reference"><a href="#cite_note-Tav-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Σελίδα: 238">: 238 </span></sup><sup id="cite_ref-T57_3-4" class="reference"><a href="#cite_note-T57-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Σελίδα: 461">: 461 </span></sup></li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}={\frac {\alpha \beta \gamma }{4R}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>α</mi> <mi>β</mi> <mi>γ</mi> </mrow> <mrow> <mn>4</mn> <mi>R</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}={\frac {\alpha \beta \gamma }{4R}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/03b0e13299b99e13de1fa1cc04213feecc41369f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:9.599ex; height:5.676ex;" alt="{\displaystyle {\rm {E}}={\frac {\alpha \beta \gamma }{4R}}}" /></span>.</dd></dl></dd></dl> <ul><li>Αν οι συντεταγμένες των κορυφών του είναι <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {A}}=(x_{\rm {A}},y_{\rm {A}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {A}}=(x_{\rm {A}},y_{\rm {A}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b94c4cf6b16e5500747cc032b58a2f9576a3772" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.083ex; height:2.843ex;" alt="{\displaystyle {\rm {A}}=(x_{\rm {A}},y_{\rm {A}})}" /></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {B}}=(x_{\rm {B}},y_{\rm {B}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {B}}=(x_{\rm {B}},y_{\rm {B}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ff251e967df754d1b4472f4d524c07ccfdc2f77" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.848ex; height:2.843ex;" alt="{\displaystyle {\rm {B}}=(x_{\rm {B}},y_{\rm {B}})}" /></span> και <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {\Gamma }}=(x_{\rm {\Gamma }},y_{\rm {\Gamma }})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> </mrow> </mrow> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> </mrow> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> </mrow> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {\Gamma }}=(x_{\rm {\Gamma }},y_{\rm {\Gamma }})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86012d058ac01ca3210d47b361609d5fd825a155" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.382ex; height:2.843ex;" alt="{\displaystyle {\rm {\Gamma }}=(x_{\rm {\Gamma }},y_{\rm {\Gamma }})}" /></span>, τότε</li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}={\frac {1}{2}}{\begin{vmatrix}x_{\rm {A}}&y_{\rm {A}}&1\\x_{\rm {B}}&y_{\rm {B}}&1\\x_{\rm {\Gamma }}&y_{\rm {\Gamma }}&1\end{vmatrix}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>|</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> </mtd> <mtd> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> </mtd> <mtd> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> </mrow> </mrow> </msub> </mtd> <mtd> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> </mrow> </mrow> </msub> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> <mo>|</mo> </mrow> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}={\frac {1}{2}}{\begin{vmatrix}x_{\rm {A}}&y_{\rm {A}}&1\\x_{\rm {B}}&y_{\rm {B}}&1\\x_{\rm {\Gamma }}&y_{\rm {\Gamma }}&1\end{vmatrix}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f95dbfab2ad2eaaac42a991afb4ef353b1e13148" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.171ex; width:20.578ex; height:9.509ex;" alt="{\displaystyle {\rm {E}}={\frac {1}{2}}{\begin{vmatrix}x_{\rm {A}}&y_{\rm {A}}&1\\x_{\rm {B}}&y_{\rm {B}}&1\\x_{\rm {\Gamma }}&y_{\rm {\Gamma }}&1\end{vmatrix}}.}" /></span></dd></dl></dd></dl> <div class="mw-heading mw-heading4"><h4 id="Ειδικά_τρίγωνα"><span id=".CE.95.CE.B9.CE.B4.CE.B9.CE.BA.CE.AC_.CF.84.CF.81.CE.AF.CE.B3.CF.89.CE.BD.CE.B1"></span>Ειδικά τρίγωνα</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&veaction=edit&section=3" title="Επεξεργασία ενότητας: Ειδικά τρίγωνα" class="mw-editsection-visualeditor"><span>Επεξεργασία</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&action=edit&section=3" title="Επεξεργαστείτε τον πηγαίο κώδικα της ενότητας: Ειδικά τρίγωνα"><span>επεξεργασία κώδικα</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>(<b><a href="/wiki/%CE%99%CF%83%CF%8C%CF%80%CE%BB%CE%B5%CF%85%CF%81%CE%BF_%CF%84%CF%81%CE%AF%CE%B3%CF%89%CE%BD%CE%BF" title="Ισόπλευρο τρίγωνο">Ισόπλευρο τρίγωνο</a></b>) Το εμβαδόν ενός ισοπλεύρου τριγώνου με μήκος πλευράς <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}" /></span> είναι<sup id="cite_ref-T57_3-5" class="reference"><a href="#cite_note-T57-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Σελίδα: 461">: 461 </span></sup></li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}={\frac {1}{4}}{\sqrt {3}}x^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}={\frac {1}{4}}{\sqrt {3}}x^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d7400ac34b3849a4c9e89c8efa0e5da09274b511" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:12.162ex; height:5.176ex;" alt="{\displaystyle {\rm {E}}={\frac {1}{4}}{\sqrt {3}}x^{2}}" /></span>.</dd></dl></dd></dl> <ul><li>(<b><a href="/wiki/%CE%9F%CF%81%CE%B8%CE%BF%CE%B3%CF%8E%CE%BD%CE%B9%CE%BF_%CF%84%CF%81%CE%AF%CE%B3%CF%89%CE%BD%CE%BF" title="Ορθογώνιο τρίγωνο">Ορθογώνιο τρίγωνο</a></b>) Το εμβαδόν ενός ορθογωνίου τριγώνου με <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {\rm {A}}}=90^{\circ }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo>=</mo> <msup> <mn>90</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {\rm {A}}}=90^{\circ }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81deff25e16a16fd5f4016b50ba24e7655efb3d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.221ex; height:2.843ex;" alt="{\displaystyle {\hat {\rm {A}}}=90^{\circ }}" /></span> είναι<sup id="cite_ref-T57_3-6" class="reference"><a href="#cite_note-T57-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Σελίδα: 460">: 460 </span></sup></li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}={\tfrac {1}{2}}\beta \cdot \gamma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <mi>β</mi> <mo>⋅</mo> <mi>γ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}={\tfrac {1}{2}}\beta \cdot \gamma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/726019217ddf8a20aa8108419a5061c66039b4dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:10.613ex; height:3.509ex;" alt="{\displaystyle {\rm {E}}={\tfrac {1}{2}}\beta \cdot \gamma }" /></span>.</dd></dl></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Τετράπλευρο"><span id=".CE.A4.CE.B5.CF.84.CF.81.CE.AC.CF.80.CE.BB.CE.B5.CF.85.CF.81.CE.BF"></span>Τετράπλευρο</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&veaction=edit&section=4" title="Επεξεργασία ενότητας: Τετράπλευρο" class="mw-editsection-visualeditor"><span>Επεξεργασία</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&action=edit&section=4" title="Επεξεργαστείτε τον πηγαίο κώδικα της ενότητας: Τετράπλευρο"><span>επεξεργασία κώδικα</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>(<b><a href="/wiki/%CE%A4%CF%8D%CF%80%CE%BF%CF%82_Bretschneider" title="Τύπος Bretschneider">Τύπος Bretschneider</a></b>) Το εμβαδόν ενός <a href="/wiki/%CE%A4%CE%B5%CF%84%CF%81%CE%AC%CF%80%CE%BB%CE%B5%CF%85%CF%81%CE%BF" title="Τετράπλευρο">τετραπλεύρου</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {AB\Gamma \Delta }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> <mi mathvariant="normal">B</mi> <mi mathvariant="normal">Γ</mi> <mi mathvariant="normal">Δ</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {AB\Gamma \Delta }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d41f17ff34c001a5cbd14e51f3287ea0592f87f6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.777ex; height:2.176ex;" alt="{\displaystyle {\rm {AB\Gamma \Delta }}}" /></span> με μήκη πλευρών <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha ,\beta ,\gamma ,\delta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mo>,</mo> <mi>β</mi> <mo>,</mo> <mi>γ</mi> <mo>,</mo> <mi>δ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha ,\beta ,\gamma ,\delta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2eb7ee31949dcce33b443132ac97f42927549e43" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.232ex; height:2.843ex;" alt="{\displaystyle \alpha ,\beta ,\gamma ,\delta }" /></span> και ημιπερίμετρο <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {\tau }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi>τ</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {\tau }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb4ca6d8d0b2a5851602233994dd32c9af530270" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.202ex; height:1.676ex;" alt="{\displaystyle {\rm {\tau }}}" /></span> είναι<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup class="reference" style="white-space:nowrap;">:207</sup></li></ul> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}={\sqrt {(\tau -\alpha )\cdot (\tau -\beta )\cdot (\tau -\gamma )\cdot (\tau -\delta )-\alpha \beta \gamma \delta \cdot \cos ^{2}\left({\tfrac {\rm {{\hat {A}}+{\hat {\Gamma }}}}{2}}\right)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo stretchy="false">(</mo> <mi>τ</mi> <mo>−</mo> <mi>α</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mo stretchy="false">(</mo> <mi>τ</mi> <mo>−</mo> <mi>β</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mo stretchy="false">(</mo> <mi>τ</mi> <mo>−</mo> <mi>γ</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mo stretchy="false">(</mo> <mi>τ</mi> <mo>−</mo> <mi>δ</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>α</mi> <mi>β</mi> <mi>γ</mi> <mi>δ</mi> <mo>⋅</mo> <msup> <mi>cos</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="normal">A</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="normal">Γ</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </mrow> <mn>2</mn> </mfrac> </mstyle> </mrow> <mo>)</mo> </mrow> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}={\sqrt {(\tau -\alpha )\cdot (\tau -\beta )\cdot (\tau -\gamma )\cdot (\tau -\delta )-\alpha \beta \gamma \delta \cdot \cos ^{2}\left({\tfrac {\rm {{\hat {A}}+{\hat {\Gamma }}}}{2}}\right)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e42ffa6fcd5bb61fecf117609e3c5b545512224b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:61.545ex; height:6.176ex;" alt="{\displaystyle {\rm {E}}={\sqrt {(\tau -\alpha )\cdot (\tau -\beta )\cdot (\tau -\gamma )\cdot (\tau -\delta )-\alpha \beta \gamma \delta \cdot \cos ^{2}\left({\tfrac {\rm {{\hat {A}}+{\hat {\Gamma }}}}{2}}\right)}}}" /></span>.</dd></dl> <ul><li>Αν οι συντεταγμένες των κορυφών του είναι <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {A}}=(x_{\rm {A}},y_{\rm {A}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {A}}=(x_{\rm {A}},y_{\rm {A}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b94c4cf6b16e5500747cc032b58a2f9576a3772" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.083ex; height:2.843ex;" alt="{\displaystyle {\rm {A}}=(x_{\rm {A}},y_{\rm {A}})}" /></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {B}}=(x_{\rm {B}},y_{\rm {B}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {B}}=(x_{\rm {B}},y_{\rm {B}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ff251e967df754d1b4472f4d524c07ccfdc2f77" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.848ex; height:2.843ex;" alt="{\displaystyle {\rm {B}}=(x_{\rm {B}},y_{\rm {B}})}" /></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {\Gamma }}=(x_{\rm {\Gamma }},y_{\rm {\Gamma }})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> </mrow> </mrow> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> </mrow> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> </mrow> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {\Gamma }}=(x_{\rm {\Gamma }},y_{\rm {\Gamma }})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86012d058ac01ca3210d47b361609d5fd825a155" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.382ex; height:2.843ex;" alt="{\displaystyle {\rm {\Gamma }}=(x_{\rm {\Gamma }},y_{\rm {\Gamma }})}" /></span> και <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {\Delta }}=(x_{\rm {\Delta }},y_{\rm {\Delta }})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> </mrow> </mrow> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> </mrow> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> </mrow> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {\Delta }}=(x_{\rm {\Delta }},y_{\rm {\Delta }})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/16902496a027cd909fc739cab3dc7a41e8748920" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.549ex; height:2.843ex;" alt="{\displaystyle {\rm {\Delta }}=(x_{\rm {\Delta }},y_{\rm {\Delta }})}" /></span>, τότε</li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}={\frac {1}{2}}{\begin{vmatrix}x_{\rm {A}}&y_{\rm {A}}&1\\x_{\rm {B}}&y_{\rm {B}}&1\\x_{\rm {\Gamma }}&y_{\rm {\Gamma }}&1\end{vmatrix}}+{\frac {1}{2}}{\begin{vmatrix}x_{\rm {B}}&y_{\rm {B}}&1\\x_{\rm {\Gamma }}&y_{\rm {\Gamma }}&1\\x_{\rm {\Delta }}&y_{\rm {\Delta }}&1\end{vmatrix}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>|</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> </mtd> <mtd> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> </mtd> <mtd> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> </mrow> </mrow> </msub> </mtd> <mtd> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> </mrow> </mrow> </msub> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> <mo>|</mo> </mrow> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>|</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> </mtd> <mtd> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> </mrow> </mrow> </msub> </mtd> <mtd> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> </mrow> </mrow> </msub> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> </mrow> </mrow> </msub> </mtd> <mtd> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> </mrow> </mrow> </msub> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> <mo>|</mo> </mrow> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}={\frac {1}{2}}{\begin{vmatrix}x_{\rm {A}}&y_{\rm {A}}&1\\x_{\rm {B}}&y_{\rm {B}}&1\\x_{\rm {\Gamma }}&y_{\rm {\Gamma }}&1\end{vmatrix}}+{\frac {1}{2}}{\begin{vmatrix}x_{\rm {B}}&y_{\rm {B}}&1\\x_{\rm {\Gamma }}&y_{\rm {\Gamma }}&1\\x_{\rm {\Delta }}&y_{\rm {\Delta }}&1\end{vmatrix}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f0dd9b231ccc4236aff7e03a87a4438f906e8ed9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.171ex; width:38.941ex; height:9.509ex;" alt="{\displaystyle {\rm {E}}={\frac {1}{2}}{\begin{vmatrix}x_{\rm {A}}&y_{\rm {A}}&1\\x_{\rm {B}}&y_{\rm {B}}&1\\x_{\rm {\Gamma }}&y_{\rm {\Gamma }}&1\end{vmatrix}}+{\frac {1}{2}}{\begin{vmatrix}x_{\rm {B}}&y_{\rm {B}}&1\\x_{\rm {\Gamma }}&y_{\rm {\Gamma }}&1\\x_{\rm {\Delta }}&y_{\rm {\Delta }}&1\end{vmatrix}}.}" /></span></dd></dl></dd></dl> <div class="mw-heading mw-heading4"><h4 id="Ειδικά_τετράπλευρα"><span id=".CE.95.CE.B9.CE.B4.CE.B9.CE.BA.CE.AC_.CF.84.CE.B5.CF.84.CF.81.CE.AC.CF.80.CE.BB.CE.B5.CF.85.CF.81.CE.B1"></span>Ειδικά τετράπλευρα</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&veaction=edit&section=5" title="Επεξεργασία ενότητας: Ειδικά τετράπλευρα" class="mw-editsection-visualeditor"><span>Επεξεργασία</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&action=edit&section=5" title="Επεξεργαστείτε τον πηγαίο κώδικα της ενότητας: Ειδικά τετράπλευρα"><span>επεξεργασία κώδικα</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>(<b><a href="/wiki/%CE%A4%CE%B5%CF%84%CF%81%CE%AC%CE%B3%CF%89%CE%BD%CE%BF" title="Τετράγωνο">Τετράγωνο</a></b>) Το εμβαδόν ενός τετραγώνου πλευράς <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}" /></span> είναι</li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}=x^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mo>=</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}=x^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a0676621eb9f4a9a8a0a95bcb2d21118d10ef94b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.065ex; height:2.676ex;" alt="{\displaystyle {\rm {E}}=x^{2}}" /></span>.</dd></dl></dd></dl> <ul><li>(<b><a href="/wiki/%CE%A1%CF%8C%CE%BC%CE%B2%CE%BF%CF%82" title="Ρόμβος">Ρόμβος</a></b>) Το εμβαδόν ενός ρόμβου είναι<sup id="cite_ref-T57_3-7" class="reference"><a href="#cite_note-T57-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Σελίδα: 463">: 463 </span></sup></li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}={\tfrac {1}{2}}\cdot \delta _{1}\cdot \delta _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <mo>⋅</mo> <msub> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>⋅</mo> <msub> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}={\tfrac {1}{2}}\cdot \delta _{1}\cdot \delta _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3e0fcecb3f6807fc630eec53279fc11ff766baa9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:13.871ex; height:3.509ex;" alt="{\displaystyle {\rm {E}}={\tfrac {1}{2}}\cdot \delta _{1}\cdot \delta _{2}}" /></span></dd></dl></dd> <dd>όπου <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta _{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta _{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/797ad61e57939cd394800dfb549e859f144f7d02" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.087ex; height:2.676ex;" alt="{\displaystyle \delta _{1}}" /></span> και <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/28152a70ffd4f5ba1fd1cf6b8f98c02c952a3002" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.087ex; height:2.676ex;" alt="{\displaystyle \delta _{2}}" /></span> είναι τα μήκη των διαγωνίων του.</dd></dl> <ul><li>(<b><a href="/wiki/%CE%A0%CE%B1%CF%81%CE%B1%CE%BB%CE%BB%CE%B7%CE%BB%CF%8C%CE%B3%CF%81%CE%B1%CE%BC%CE%BC%CE%BF" title="Παραλληλόγραμμο">Παραλληλόγραμμο</a></b>) Το εμβαδόν ενός παραλληλογράμμου είναι<sup id="cite_ref-T57_3-8" class="reference"><a href="#cite_note-T57-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Σελίδα: 458">: 458 </span></sup></li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}=\beta \cdot \upsilon }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mo>=</mo> <mi>β</mi> <mo>⋅</mo> <mi>υ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}=\beta \cdot \upsilon }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a6196c77ce41b339974f7edd0bb9585599ff9284" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.948ex; height:2.509ex;" alt="{\displaystyle {\rm {E}}=\beta \cdot \upsilon }" /></span></dd></dl></dd> <dd>όπου <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.332ex; height:2.509ex;" alt="{\displaystyle \beta }" /></span> είναι το μήκος της μίας πλευράς (αποκαλούμενης <i>βάσης</i>) και <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \upsilon }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>υ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \upsilon }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3d9773c30e2bda2ecb0af8fa63f9e0e537f0fc4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.255ex; height:1.676ex;" alt="{\displaystyle \upsilon }" /></span> το μήκος της απόστασης μεταξή των δύο παράλληλων βάσεων (αποκαλούμενου ύψους).</dd></dl> <ul><li>(<b><a href="/wiki/%CE%A4%CF%81%CE%B1%CF%80%CE%AD%CE%B6%CE%B9%CE%BF" title="Τραπέζιο">Τραπέζιο</a></b>) Το εμβαδόν ενός τραπεζίου είναι<sup id="cite_ref-T57_3-9" class="reference"><a href="#cite_note-T57-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Σελίδα: 464">: 464 </span></sup></li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}={\tfrac {1}{2}}\cdot (B+\beta )\cdot \upsilon }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <mo>⋅</mo> <mo stretchy="false">(</mo> <mi>B</mi> <mo>+</mo> <mi>β</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>υ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}={\tfrac {1}{2}}\cdot (B+\beta )\cdot \upsilon }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/683582504feabb9a673f05132ff707cf495389e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:18.699ex; height:3.509ex;" alt="{\displaystyle {\rm {E}}={\tfrac {1}{2}}\cdot (B+\beta )\cdot \upsilon }" /></span>,</dd></dl></dd> <dd>όπου <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" /></span> και <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.332ex; height:2.509ex;" alt="{\displaystyle \beta }" /></span> είναι τα μήκη των δύο παράλληλων πλευρών του (αποκαλούμενες ως <i>βάση</i> και <i>μικρή βάση</i> αντίστοιχα) και <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \upsilon }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>υ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \upsilon }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3d9773c30e2bda2ecb0af8fa63f9e0e537f0fc4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.255ex; height:1.676ex;" alt="{\displaystyle \upsilon }" /></span> το ύψος του, δηλαδή η απόσταση ανάμεσα στις δύο παράλληλες.</dd></dl> <ul><li>Το εμβαδόν ενός τραπεζίου με πλευρές <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha ,\beta ,\gamma ,\delta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mo>,</mo> <mi>β</mi> <mo>,</mo> <mi>γ</mi> <mo>,</mo> <mi>δ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha ,\beta ,\gamma ,\delta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2eb7ee31949dcce33b443132ac97f42927549e43" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.232ex; height:2.843ex;" alt="{\displaystyle \alpha ,\beta ,\gamma ,\delta }" /></span> και ημιπερίμετρο <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>τ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38a7dcde9730ef0853809fefc18d88771f95206c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.202ex; height:1.676ex;" alt="{\displaystyle \tau }" /></span> είναι<sup id="cite_ref-T57_3-10" class="reference"><a href="#cite_note-T57-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Σελίδα: 465">: 465 </span></sup></li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}={\frac {\alpha +\beta }{\alpha -\beta }}\cdot {\sqrt {(\tau -\alpha )(\tau -\beta )(\tau -\beta -\gamma )(\tau -\beta -\delta )}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>α</mi> <mo>+</mo> <mi>β</mi> </mrow> <mrow> <mi>α</mi> <mo>−</mo> <mi>β</mi> </mrow> </mfrac> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo stretchy="false">(</mo> <mi>τ</mi> <mo>−</mo> <mi>α</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>τ</mi> <mo>−</mo> <mi>β</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>τ</mi> <mo>−</mo> <mi>β</mi> <mo>−</mo> <mi>γ</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>τ</mi> <mo>−</mo> <mi>β</mi> <mo>−</mo> <mi>δ</mi> <mo stretchy="false">)</mo> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}={\frac {\alpha +\beta }{\alpha -\beta }}\cdot {\sqrt {(\tau -\alpha )(\tau -\beta )(\tau -\beta -\gamma )(\tau -\beta -\delta )}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e3d9a0a28466506633a52bf4d4696139b5e7fc8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:52.062ex; height:5.843ex;" alt="{\displaystyle {\rm {E}}={\frac {\alpha +\beta }{\alpha -\beta }}\cdot {\sqrt {(\tau -\alpha )(\tau -\beta )(\tau -\beta -\gamma )(\tau -\beta -\delta )}}}" /></span>.</dd></dl></dd></dl> <ul><li>(<b><a href="/wiki/%CE%A4%CF%8D%CF%80%CE%BF%CF%82_%CE%92%CF%81%CE%B1%CF%87%CE%BC%CE%B1%CE%B3%CE%BA%CE%BF%CF%8D%CF%80%CF%84%CE%B1" title="Τύπος Βραχμαγκούπτα">Τύπος Βραχμαγκούπτα</a></b>) Το εμβαδόν ενός <a href="/wiki/%CE%95%CE%B3%CE%B3%CF%81%CE%AC%CF%88%CE%B9%CE%BC%CE%BF_%CF%84%CE%B5%CF%84%CF%81%CE%AC%CF%80%CE%BB%CE%B5%CF%85%CF%81%CE%BF" class="mw-redirect" title="Εγγράψιμο τετράπλευρο">εγγράψιμου τετραπλεύρου</a> δίνεται από</li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}={\sqrt {(\tau -\alpha )\cdot (\tau -\beta )\cdot (\tau -\gamma )\cdot (\tau -\delta )}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo stretchy="false">(</mo> <mi>τ</mi> <mo>−</mo> <mi>α</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mo stretchy="false">(</mo> <mi>τ</mi> <mo>−</mo> <mi>β</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mo stretchy="false">(</mo> <mi>τ</mi> <mo>−</mo> <mi>γ</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mo stretchy="false">(</mo> <mi>τ</mi> <mo>−</mo> <mi>δ</mi> <mo stretchy="false">)</mo> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}={\sqrt {(\tau -\alpha )\cdot (\tau -\beta )\cdot (\tau -\gamma )\cdot (\tau -\delta )}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f811aa3d69f0ea087ba218c8c0c9adb310b0db0c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:40.58ex; height:4.843ex;" alt="{\displaystyle {\rm {E}}={\sqrt {(\tau -\alpha )\cdot (\tau -\beta )\cdot (\tau -\gamma )\cdot (\tau -\delta )}}}" /></span></dd></dl></dd> <dd>όπου <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }" /></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.332ex; height:2.509ex;" alt="{\displaystyle \beta }" /></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \gamma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>γ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \gamma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a223c880b0ce3da8f64ee33c4f0010beee400b1a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.262ex; height:2.176ex;" alt="{\displaystyle \gamma }" /></span> και <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5321cfa797202b3e1f8620663ff43c4660ea03a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:2.343ex;" alt="{\displaystyle \delta }" /></span> είναι τα μήκη των πλευρών του και <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau ={\tfrac {1}{2}}\cdot (\alpha +\beta +\gamma +\delta )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>τ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <mo>⋅</mo> <mo stretchy="false">(</mo> <mi>α</mi> <mo>+</mo> <mi>β</mi> <mo>+</mo> <mi>γ</mi> <mo>+</mo> <mi>δ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau ={\tfrac {1}{2}}\cdot (\alpha +\beta +\gamma +\delta )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/25383b4925d8f2ef50280eb357acd73ac4f886df" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:23.099ex; height:3.509ex;" alt="{\displaystyle \tau ={\tfrac {1}{2}}\cdot (\alpha +\beta +\gamma +\delta )}" /></span> η ημιπερίμετρός του.</dd></dl> <div class="mw-heading mw-heading3"><h3 id="Κανονικό_πολύγωνο"><span id=".CE.9A.CE.B1.CE.BD.CE.BF.CE.BD.CE.B9.CE.BA.CF.8C_.CF.80.CE.BF.CE.BB.CF.8D.CE.B3.CF.89.CE.BD.CE.BF"></span>Κανονικό πολύγωνο</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&veaction=edit&section=6" title="Επεξεργασία ενότητας: Κανονικό πολύγωνο" class="mw-editsection-visualeditor"><span>Επεξεργασία</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&action=edit&section=6" title="Επεξεργαστείτε τον πηγαίο κώδικα της ενότητας: Κανονικό πολύγωνο"><span>επεξεργασία κώδικα</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Το εμβαδόν ενός κανονικού <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}" /></span>-γώνου με πλευρά μήκους <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}" /></span> είναι</li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}={\frac {1}{4}}nx^{2}\cdot \cot(\pi /n)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> <mi>n</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⋅</mo> <mi>cot</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>n</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}={\frac {1}{4}}nx^{2}\cdot \cot(\pi /n)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/76fefd4fa83321d3c080404fa57ab65f835c4581" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:20.936ex; height:5.176ex;" alt="{\displaystyle {\rm {E}}={\frac {1}{4}}nx^{2}\cdot \cot(\pi /n)}" /></span>.</dd></dl></dd></dl> <ul><li>Το εμβαδόν ενός κανονικού <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}" /></span>-γώνου με ημιπερίμετρο <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>τ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38a7dcde9730ef0853809fefc18d88771f95206c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.202ex; height:1.676ex;" alt="{\displaystyle \tau }" /></span> είναι</li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}={\frac {1}{n}}\cdot \tau \cdot \cot(\pi /n)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> </mrow> <mo>⋅</mo> <mi>τ</mi> <mo>⋅</mo> <mi>cot</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>n</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}={\frac {1}{n}}\cdot \tau \cdot \cot(\pi /n)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1e264cfd659d594b56944fc59ee718f3881e9c62" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:20.27ex; height:5.176ex;" alt="{\displaystyle {\rm {E}}={\frac {1}{n}}\cdot \tau \cdot \cot(\pi /n)}" /></span></dd></dl></dd></dl> <ul><li>Το εμβαδόν ενός κανονικού <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}" /></span>-γώνου είναι</li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}={\frac {1}{2}}nR^{2}\cdot \sin(2\pi /n)=nr^{2}\tan(\pi /n)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>n</mi> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>n</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>n</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>tan</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>n</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}={\frac {1}{2}}nR^{2}\cdot \sin(2\pi /n)=nr^{2}\tan(\pi /n)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/573ef7929e04c1d1b4c10a1e748e073273fcb19b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:38.33ex; height:5.176ex;" alt="{\displaystyle {\rm {E}}={\frac {1}{2}}nR^{2}\cdot \sin(2\pi /n)=nr^{2}\tan(\pi /n)}" /></span></dd></dl></dd> <dd>όπου <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}" /></span> είναι η ακτίνα του περιγεγραμμένου του κύκλου, και <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}" /></span> είναι η ακτίνα του εγγεγραμμένου του κύκλου.</dd></dl> <ul><li>Το εμβαδόν ενός κανονικού <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}" /></span>-γώνου είναι<sup id="cite_ref-T57_3-11" class="reference"><a href="#cite_note-T57-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Σελίδα: 466">: 466 </span></sup></li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}=\tau \cdot \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mo>=</mo> <mi>τ</mi> <mo>⋅</mo> <mi>ρ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}=\tau \cdot \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b95ea4355b2aa644c013f771ebbc237759a0fd45" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.764ex; height:2.676ex;" alt="{\displaystyle {\rm {E}}=\tau \cdot \rho }" /></span></dd></dl></dd> <dd>όπου <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}" /></span> είναι η ακτίνα του εγγεγραμμένου του κύκλου, και <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>τ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38a7dcde9730ef0853809fefc18d88771f95206c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.202ex; height:1.676ex;" alt="{\displaystyle \tau }" /></span> η ημιπερίμετρος του.</dd></dl> <div class="mw-heading mw-heading4"><h4 id="Ειδικές_περιπτώσεις"><span id=".CE.95.CE.B9.CE.B4.CE.B9.CE.BA.CE.AD.CF.82_.CF.80.CE.B5.CF.81.CE.B9.CF.80.CF.84.CF.8E.CF.83.CE.B5.CE.B9.CF.82"></span>Ειδικές περιπτώσεις</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&veaction=edit&section=7" title="Επεξεργασία ενότητας: Ειδικές περιπτώσεις" class="mw-editsection-visualeditor"><span>Επεξεργασία</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&action=edit&section=7" title="Επεξεργαστείτε τον πηγαίο κώδικα της ενότητας: Ειδικές περιπτώσεις"><span>επεξεργασία κώδικα</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>(<b><a href="/wiki/%CE%9A%CE%B1%CE%BD%CE%BF%CE%BD%CE%B9%CE%BA%CF%8C_%CE%B5%CE%BE%CE%AC%CE%B3%CF%89%CE%BD%CE%BF" class="mw-redirect" title="Κανονικό εξάγωνο">Κανονικό εξάγωνο</a></b>) Το εμβαδόν ενός κανονικού εξαγώνου πλευράς <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}" /></span> δίνεται από</li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}={\frac {3}{2}}{\sqrt {3}}x^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}={\frac {3}{2}}{\sqrt {3}}x^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e8fa91f68f664defccf8b0650b45becdc59c3105" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:12.162ex; height:5.176ex;" alt="{\displaystyle {\rm {E}}={\frac {3}{2}}{\sqrt {3}}x^{2}}" /></span>.</dd></dl></dd></dl> <ul><li>(<b><a href="/wiki/%CE%9A%CE%B1%CE%BD%CE%BF%CE%BD%CE%B9%CE%BA%CF%8C_%CE%BF%CE%BA%CF%84%CE%AC%CE%B3%CF%89%CE%BD%CE%BF" class="mw-redirect" title="Κανονικό οκτάγωνο">Κανονικό οκτάγωνο</a></b>) Το εμβαδόν ενός κανονικού οκταγώνου πλευράς <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}" /></span> δίνεται από</li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}=2(1+{\sqrt {2}})x^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mo>=</mo> <mn>2</mn> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <mo stretchy="false">)</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}=2(1+{\sqrt {2}})x^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4bbf138665866eb1c9aa012dd9c62f3a5f19a61b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.138ex; height:3.176ex;" alt="{\displaystyle {\rm {E}}=2(1+{\sqrt {2}})x^{2}}" /></span></dd></dl></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Κύκλος_και_κυκλικός_τομέας"><span id=".CE.9A.CF.8D.CE.BA.CE.BB.CE.BF.CF.82_.CE.BA.CE.B1.CE.B9_.CE.BA.CF.85.CE.BA.CE.BB.CE.B9.CE.BA.CF.8C.CF.82_.CF.84.CE.BF.CE.BC.CE.AD.CE.B1.CF.82"></span>Κύκλος και κυκλικός τομέας</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&veaction=edit&section=8" title="Επεξεργασία ενότητας: Κύκλος και κυκλικός τομέας" class="mw-editsection-visualeditor"><span>Επεξεργασία</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&action=edit&section=8" title="Επεξεργαστείτε τον πηγαίο κώδικα της ενότητας: Κύκλος και κυκλικός τομέας"><span>επεξεργασία κώδικα</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Το εμβαδόν ενός <a href="/wiki/%CE%9A%CF%8D%CE%BA%CE%BB%CE%BF%CF%82" title="Κύκλος">κύκλου</a> είναι ίσο με<sup id="cite_ref-T57_3-12" class="reference"><a href="#cite_note-T57-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Σελίδα: 474">: 474 </span></sup></li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}=\pi r^{2}={\frac {\pi d^{2}}{4}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mo>=</mo> <mi>π</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>π</mi> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mn>4</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}=\pi r^{2}={\frac {\pi d^{2}}{4}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/79f38ede7a7b863772453eea5db9e801a87baa48" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:15.655ex; height:5.676ex;" alt="{\displaystyle {\rm {E}}=\pi r^{2}={\frac {\pi d^{2}}{4}}}" /></span>,</dd></dl></dd> <dd>όπου <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}" /></span> είναι η ακτίνα του και <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d=2r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo>=</mo> <mn>2</mn> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d=2r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aedbeca9223f2026e9d51322e86d67e10c092792" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.525ex; height:2.176ex;" alt="{\displaystyle d=2r}" /></span> είναι η <a href="/wiki/%CE%94%CE%B9%CE%AC%CE%BC%CE%B5%CF%84%CF%81%CE%BF%CF%82" title="Διάμετρος">διάμετρος</a> του.</dd></dl> <ul><li>Το εμβαδόν ενός <a href="/wiki/%CE%9A%CF%85%CE%BA%CE%BB%CE%B9%CE%BA%CF%8C%CF%82_%CF%84%CE%BF%CE%BC%CE%AD%CE%B1%CF%82" title="Κυκλικός τομέας">κυκλικού τομέα</a> είναι<sup id="cite_ref-T57_3-13" class="reference"><a href="#cite_note-T57-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Σελίδα: 474">: 474 </span></sup></li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}={\frac {\theta }{2}}r^{2}={\frac {\Pi \cdot r}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>θ</mi> <mn>2</mn> </mfrac> </mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Π</mi> <mo>⋅</mo> <mi>r</mi> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}={\frac {\theta }{2}}r^{2}={\frac {\Pi \cdot r}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5b81eb47dabb2c3b82fc262288c99dec0b7b8b47" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:17.188ex; height:5.343ex;" alt="{\displaystyle {\rm {E}}={\frac {\theta }{2}}r^{2}={\frac {\Pi \cdot r}{2}}}" /></span></dd></dl></dd> <dd>όπου <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}" /></span> είναι η ακτίνα του κύκλου, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e5ab2664b422d53eb0c7df3b87e1360d75ad9af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }" /></span> είναι η γωνία του (σε <a href="/wiki/%CE%91%CE%BA%CF%84%CE%AF%CE%BD%CE%B9%CE%B1" class="mw-redirect" title="Ακτίνια">ακτίνια</a>), και <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eed3e3db6cc2028a183af948212ed2551d25c954" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle \Pi }" /></span> η περίμετρός του.</dd></dl> <div class="mw-heading mw-heading2"><h2 id="Επιφάνεια_γεωματερικών_στερεών"><span id=".CE.95.CF.80.CE.B9.CF.86.CE.AC.CE.BD.CE.B5.CE.B9.CE.B1_.CE.B3.CE.B5.CF.89.CE.BC.CE.B1.CF.84.CE.B5.CF.81.CE.B9.CE.BA.CF.8E.CE.BD_.CF.83.CF.84.CE.B5.CF.81.CE.B5.CF.8E.CE.BD"></span>Επιφάνεια γεωματερικών στερεών</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&veaction=edit&section=9" title="Επεξεργασία ενότητας: Επιφάνεια γεωματερικών στερεών" class="mw-editsection-visualeditor"><span>Επεξεργασία</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&action=edit&section=9" title="Επεξεργαστείτε τον πηγαίο κώδικα της ενότητας: Επιφάνεια γεωματερικών στερεών"><span>επεξεργασία κώδικα</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Κύλινδρος"><span id=".CE.9A.CF.8D.CE.BB.CE.B9.CE.BD.CE.B4.CF.81.CE.BF.CF.82"></span>Κύλινδρος</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&veaction=edit&section=10" title="Επεξεργασία ενότητας: Κύλινδρος" class="mw-editsection-visualeditor"><span>Επεξεργασία</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&action=edit&section=10" title="Επεξεργαστείτε τον πηγαίο κώδικα της ενότητας: Κύλινδρος"><span>επεξεργασία κώδικα</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Το εμβαδόν της παράπλευρης επιφάνειας ενός <a href="/wiki/%CE%9A%CF%8D%CE%BB%CE%B9%CE%BD%CE%B4%CF%81%CE%BF%CF%82_(%CE%B3%CE%B5%CF%89%CE%BC%CE%B5%CF%84%CF%81%CE%AF%CE%B1)" title="Κύλινδρος (γεωμετρία)">κυλίνδρου</a> δίνεται από </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}_{\text{π}}=2\pi r\cdot \upsilon }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>π</mtext> </mrow> </msub> <mo>=</mo> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mo>⋅</mo> <mi>υ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}_{\text{π}}=2\pi r\cdot \upsilon }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2700c9bf52e4187398875a8bbaf4d198b0dfe48d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.333ex; height:2.509ex;" alt="{\displaystyle {\rm {E}}_{\text{π}}=2\pi r\cdot \upsilon }" /></span>,</dd></dl> <p>και το εμβαδόν της συνολικής επιφάνειας του από<sup id="cite_ref-T57_3-14" class="reference"><a href="#cite_note-T57-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference" style="white-space:nowrap;">:738</sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}_{\text{ολ}}=2\pi r(r+\upsilon )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>ολ</mtext> </mrow> </msub> <mo>=</mo> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo>+</mo> <mi>υ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}_{\text{ολ}}=2\pi r(r+\upsilon )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/84d2977f54258a019b006bce5f52f6453e808632" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.166ex; height:2.843ex;" alt="{\displaystyle {\rm {E}}_{\text{ολ}}=2\pi r(r+\upsilon )}" /></span>,</dd></dl> <p>όπου <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}" /></span> είναι η ακτίνα και <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \upsilon }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>υ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \upsilon }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3d9773c30e2bda2ecb0af8fa63f9e0e537f0fc4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.255ex; height:1.676ex;" alt="{\displaystyle \upsilon }" /></span> το ύψος του. </p> <div class="mw-heading mw-heading3"><h3 id="Σφαίρα"><span id=".CE.A3.CF.86.CE.B1.CE.AF.CF.81.CE.B1"></span>Σφαίρα</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&veaction=edit&section=11" title="Επεξεργασία ενότητας: Σφαίρα" class="mw-editsection-visualeditor"><span>Επεξεργασία</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&action=edit&section=11" title="Επεξεργαστείτε τον πηγαίο κώδικα της ενότητας: Σφαίρα"><span>επεξεργασία κώδικα</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Το εμβαδόν της συνολικής επιφάνειας μίας <a href="/wiki/%CE%A3%CF%86%CE%B1%CE%AF%CF%81%CE%B1" title="Σφαίρα">σφαίρας</a> δίνεται από<sup id="cite_ref-T57_3-15" class="reference"><a href="#cite_note-T57-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Σελίδα: 780">: 780 </span></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}_{\text{σφ}}=4\pi r^{2}=\pi d^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>σφ</mtext> </mrow> </msub> <mo>=</mo> <mn>4</mn> <mi>π</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mi>π</mi> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}_{\text{σφ}}=4\pi r^{2}=\pi d^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fab76608c68a9e7cfb2312966abf25eb0970eca5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:18.227ex; height:3.343ex;" alt="{\displaystyle {\rm {E}}_{\text{σφ}}=4\pi r^{2}=\pi d^{2}}" /></span>,</dd></dl> <p>όπου <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}" /></span> είναι η ακτίνα της και <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d=2r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo>=</mo> <mn>2</mn> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d=2r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aedbeca9223f2026e9d51322e86d67e10c092792" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.525ex; height:2.176ex;" alt="{\displaystyle d=2r}" /></span> η διάμετρός της. </p> <div class="mw-heading mw-heading3"><h3 id="Πυραμίδα"><span id=".CE.A0.CF.85.CF.81.CE.B1.CE.BC.CE.AF.CE.B4.CE.B1"></span>Πυραμίδα</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&veaction=edit&section=12" title="Επεξεργασία ενότητας: Πυραμίδα" class="mw-editsection-visualeditor"><span>Επεξεργασία</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&action=edit&section=12" title="Επεξεργαστείτε τον πηγαίο κώδικα της ενότητας: Πυραμίδα"><span>επεξεργασία κώδικα</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Το εμβαδόν της παράπλευρης επιφάνειας μίας <a href="/wiki/%CE%A0%CF%85%CF%81%CE%B1%CE%BC%CE%AF%CE%B4%CE%B1_(%CE%B3%CE%B5%CF%89%CE%BC%CE%B5%CF%84%CF%81%CE%AF%CE%B1)" title="Πυραμίδα (γεωμετρία)">πυραμίδας</a> δίνεται από<sup id="cite_ref-T57_3-16" class="reference"><a href="#cite_note-T57-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Σελίδα: 683">: 683 </span></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}_{\text{π}}={\tfrac {1}{2}}\Pi \cdot \upsilon }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>π</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <mi mathvariant="normal">Π</mi> <mo>⋅</mo> <mi>υ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}_{\text{π}}={\tfrac {1}{2}}\Pi \cdot \upsilon }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e7cd025627acf9bff0477c7ccb93028298abed7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:12.191ex; height:3.509ex;" alt="{\displaystyle {\rm {E}}_{\text{π}}={\tfrac {1}{2}}\Pi \cdot \upsilon }" /></span></dd></dl> <p>και το εμβαδόν της συνολικής της επιφάνειας από </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}_{\text{ολ}}={\rm {E}}_{B}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>ολ</mtext> </mrow> </msub> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}_{\text{ολ}}={\rm {E}}_{B}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/40143fe1e8f30301b66171c8bb8c960672f2555c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.732ex; height:2.509ex;" alt="{\displaystyle {\rm {E}}_{\text{ολ}}={\rm {E}}_{B}}" /></span>,</dd></dl> <p>όπου <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}_{B}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}_{B}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e10de3b6d41feac70e8edb8006d3cd19e85b1dfc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.062ex; height:2.509ex;" alt="{\displaystyle {\rm {E}}_{B}}" /></span> είναι το εμβαδόν της επιφάνειας της βάσης, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eed3e3db6cc2028a183af948212ed2551d25c954" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle \Pi }" /></span> είναι η περίμετρος της βάσης και <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \upsilon }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>υ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \upsilon }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3d9773c30e2bda2ecb0af8fa63f9e0e537f0fc4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.255ex; height:1.676ex;" alt="{\displaystyle \upsilon }" /></span> το παράπλευρο ύψος. </p> <div class="mw-heading mw-heading3"><h3 id="Κώνος"><span id=".CE.9A.CF.8E.CE.BD.CE.BF.CF.82"></span>Κώνος</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&veaction=edit&section=13" title="Επεξεργασία ενότητας: Κώνος" class="mw-editsection-visualeditor"><span>Επεξεργασία</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&action=edit&section=13" title="Επεξεργαστείτε τον πηγαίο κώδικα της ενότητας: Κώνος"><span>επεξεργασία κώδικα</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Το εμβαδόν της παράπλευρης επιφάνειας ενός <a href="/wiki/%CE%9A%CF%8E%CE%BD%CE%BF%CF%82" title="Κώνος">κώνου</a> είναι<sup id="cite_ref-T57_3-17" class="reference"><a href="#cite_note-T57-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Σελίδα: 747">: 747 </span></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}_{\text{π}}=\pi r\ell =\pi r{\sqrt {r^{2}+\upsilon ^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>π</mtext> </mrow> </msub> <mo>=</mo> <mi>π</mi> <mi>r</mi> <mi>ℓ</mi> <mo>=</mo> <mi>π</mi> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>υ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}_{\text{π}}=\pi r\ell =\pi r{\sqrt {r^{2}+\upsilon ^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2cf32da8a1f48a8cbfcd711327eb3323c6531994" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:24.262ex; height:3.509ex;" alt="{\displaystyle {\rm {E}}_{\text{π}}=\pi r\ell =\pi r{\sqrt {r^{2}+\upsilon ^{2}}}}" /></span></dd></dl> <p>και της συνολικής του επιφάνειας είναι </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {E}}_{\text{ολ}}=\pi r(r+\ell )=\pi r(r+{\sqrt {r^{2}+\upsilon ^{2}}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>ολ</mtext> </mrow> </msub> <mo>=</mo> <mi>π</mi> <mi>r</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo>+</mo> <mi>ℓ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>π</mi> <mi>r</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>υ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {E}}_{\text{ολ}}=\pi r(r+\ell )=\pi r(r+{\sqrt {r^{2}+\upsilon ^{2}}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a435eead510cc4434dc3ae61d974f7a3af5a84a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:36.472ex; height:3.509ex;" alt="{\displaystyle {\rm {E}}_{\text{ολ}}=\pi r(r+\ell )=\pi r(r+{\sqrt {r^{2}+\upsilon ^{2}}})}" /></span>,</dd></dl> <p>όπου <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}" /></span> είναι η ακτίνα της βάσης, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \upsilon }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>υ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \upsilon }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3d9773c30e2bda2ecb0af8fa63f9e0e537f0fc4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.255ex; height:1.676ex;" alt="{\displaystyle \upsilon }" /></span> το ύψος του κώνου, και <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ell }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ℓ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ell }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f066e981e530bacc07efc6a10fa82deee985929e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.97ex; height:2.176ex;" alt="{\displaystyle \ell }" /></span> η ακμή του. </p> <div class="mw-heading mw-heading2"><h2 id="Μεταξύ_όμοιων_σχημάτων"><span id=".CE.9C.CE.B5.CF.84.CE.B1.CE.BE.CF.8D_.CF.8C.CE.BC.CE.BF.CE.B9.CF.89.CE.BD_.CF.83.CF.87.CE.B7.CE.BC.CE.AC.CF.84.CF.89.CE.BD"></span>Μεταξύ όμοιων σχημάτων</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&veaction=edit&section=14" title="Επεξεργασία ενότητας: Μεταξύ όμοιων σχημάτων" class="mw-editsection-visualeditor"><span>Επεξεργασία</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&action=edit&section=14" title="Επεξεργαστείτε τον πηγαίο κώδικα της ενότητας: Μεταξύ όμοιων σχημάτων"><span>επεξεργασία κώδικα</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r9961950">.mw-parser-output .math_theorem{margin:1em 2em;padding:0.5em 1em 0.4em;border:1px solid #aaa;overflow:hidden}@media(max-width:500px){.mw-parser-output .math_theorem{margin:1em 0em;padding:0.5em 0.5em 0.4em}}</style><div class="math_theorem" style=""> <p><strong class="theorem-name">Θεώρημα</strong><span class="theoreme-tiret"> — </span>Έστω δύο <a href="/w/index.php?title=%CE%9F%CE%BC%CE%BF%CE%B9%CF%8C%CF%84%CE%B7%CF%84%CE%B1_(%CE%B3%CE%B5%CF%89%CE%BC%CE%B5%CF%84%CF%81%CE%AF%CE%B1)&action=edit&redlink=1" class="new" title="Ομοιότητα (γεωμετρία) (δεν έχει γραφτεί ακόμα)">όμοια</a> πολύγωνα <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Sigma _{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Sigma _{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d37ee4ac26b75c4bca37e546fcc9859f3e45adf9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.732ex; height:2.509ex;" alt="{\displaystyle \Sigma _{1}}" /></span> και <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Sigma _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Sigma _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4f8624a29dcd9e745a2061940b76c434779c83d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.732ex; height:2.509ex;" alt="{\displaystyle \Sigma _{2}}" /></span> με λόγο ομοιότητας <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b43d0ea3c9c025af1be9128e62a18fa74bedda2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.355ex; height:2.176ex;" alt="{\displaystyle \lambda }" /></span>. Τότε ο λόγος των εμβαδών τους ικανοποιεί<sup id="cite_ref-T57_3-18" class="reference"><a href="#cite_note-T57-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Σελίδα: 487">: 487 </span></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {{\rm {E}}_{1}}{{\rm {E}}_{2}}}=\lambda ^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <msup> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {{\rm {E}}_{1}}{{\rm {E}}_{2}}}=\lambda ^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f8b802429b72cf47f21db2f6f0185b534522aaff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:8.981ex; height:5.509ex;" alt="{\displaystyle {\frac {{\rm {E}}_{1}}{{\rm {E}}_{2}}}=\lambda ^{2}}" /></span>.</dd></dl> </div> <div class="mw-heading mw-heading2"><h2 id="Δείτε_επίσης"><span id=".CE.94.CE.B5.CE.AF.CF.84.CE.B5_.CE.B5.CF.80.CE.AF.CF.83.CE.B7.CF.82"></span>Δείτε επίσης</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&veaction=edit&section=15" title="Επεξεργασία ενότητας: Δείτε επίσης" class="mw-editsection-visualeditor"><span>Επεξεργασία</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&action=edit&section=15" title="Επεξεργαστείτε τον πηγαίο κώδικα της ενότητας: Δείτε επίσης"><span>επεξεργασία κώδικα</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%CE%A0%CE%B5%CF%81%CE%AF%CE%BC%CE%B5%CF%84%CF%81%CE%BF%CF%82" title="Περίμετρος">Περίμετρος</a></li> <li><a href="/wiki/%CE%8C%CE%B3%CE%BA%CE%BF%CF%82" title="Όγκος">Όγκος</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Περαιτέρω_ανάγνωση"><span id=".CE.A0.CE.B5.CF.81.CE.B1.CE.B9.CF.84.CE.AD.CF.81.CF.89_.CE.B1.CE.BD.CE.AC.CE.B3.CE.BD.CF.89.CF.83.CE.B7"></span>Περαιτέρω ανάγνωση</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&veaction=edit&section=16" title="Επεξεργασία ενότητας: Περαιτέρω ανάγνωση" class="mw-editsection-visualeditor"><span>Επεξεργασία</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&action=edit&section=16" title="Επεξεργαστείτε τον πηγαίο κώδικα της ενότητας: Περαιτέρω ανάγνωση"><span>επεξεργασία κώδικα</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Ελληνικά_άρθρα"><span id=".CE.95.CE.BB.CE.BB.CE.B7.CE.BD.CE.B9.CE.BA.CE.AC_.CE.AC.CF.81.CE.B8.CF.81.CE.B1"></span>Ελληνικά άρθρα</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&veaction=edit&section=17" title="Επεξεργασία ενότητας: Ελληνικά άρθρα" class="mw-editsection-visualeditor"><span>Επεξεργασία</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&action=edit&section=17" title="Επεξεργαστείτε τον πηγαίο κώδικα της ενότητας: Ελληνικά άρθρα"><span>επεξεργασία κώδικα</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="citation Journal">Καρδαμίτσης, Σπύρος (Οκτωβρίου 2021). <a rel="nofollow" class="external text" href="http://niobe.hms.gr/sites/default/files/subsites/problems/material/EYKLEIDHS_B_t122_2021.pdf">«Εμβαδά ευθυγράμμων σχημάτων»</a>. <i><a href="/wiki/%CE%95%CF%85%CE%BA%CE%BB%CE%B5%CE%AF%CE%B4%CE%B7%CF%82_%CE%92%CE%84" title="Ευκλείδης Β΄">Ευκλείδης Β΄</a></i> (122): 36-38<span class="printonly">. <a rel="nofollow" class="external free" href="http://niobe.hms.gr/sites/default/files/subsites/problems/material/EYKLEIDHS_B_t122_2021.pdf">http://niobe.hms.gr/sites/default/files/subsites/problems/material/EYKLEIDHS_B_t122_2021.pdf</a></span>.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CE%AC+%CE%B5%CF%85%CE%B8%CF%85%CE%B3%CF%81%CE%AC%CE%BC%CE%BC%CF%89%CE%BD+%CF%83%CF%87%CE%B7%CE%BC%CE%AC%CF%84%CF%89%CE%BD&rft.jtitle=%5B%5B%CE%95%CF%85%CE%BA%CE%BB%CE%B5%CE%AF%CE%B4%CE%B7%CF%82+%CE%92%CE%84%5D%5D&rft.aulast=%CE%9A%CE%B1%CF%81%CE%B4%CE%B1%CE%BC%CE%AF%CF%84%CF%83%CE%B7%CF%82&rft.aufirst=%CE%A3%CF%80%CF%8D%CF%81%CE%BF%CF%82&rft.au=%CE%9A%CE%B1%CF%81%CE%B4%CE%B1%CE%BC%CE%AF%CF%84%CF%83%CE%B7%CF%82%2C%26%2332%3B%CE%A3%CF%80%CF%8D%CF%81%CE%BF%CF%82&rft.date=%CE%9F%CE%BA%CF%84%CF%89%CE%B2%CF%81%CE%AF%CE%BF%CF%85+2021&rft.issue=122&rft.pages=36-38&rft_id=http%3A%2F%2Fniobe.hms.gr%2Fsites%2Fdefault%2Ffiles%2Fsubsites%2Fproblems%2Fmaterial%2FEYKLEIDHS_B_t122_2021.pdf&rfr_id=info:sid/el.wikipedia.org:%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD"><span style="display: none;"> </span></span></li> <li><span class="citation Journal"><a rel="nofollow" class="external text" href="http://niobe.hms.gr/apothema/?s=sa&i=2918">«Παραδείγματα και ασκήσεις στα εμβαδά πολυγώνων»</a>. <i><a href="/wiki/%CE%95%CF%85%CE%BA%CE%BB%CE%B5%CE%AF%CE%B4%CE%B7%CF%82_%CE%92%CE%84" title="Ευκλείδης Β΄">Ευκλείδης Β΄</a></i> (2): 28-30. 1977<span class="printonly">. <a rel="nofollow" class="external free" href="http://niobe.hms.gr/apothema/?s=sa&i=2918">http://niobe.hms.gr/apothema/?s=sa&i=2918</a></span>.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=%CE%A0%CE%B1%CF%81%CE%B1%CE%B4%CE%B5%CE%AF%CE%B3%CE%BC%CE%B1%CF%84%CE%B1+%CE%BA%CE%B1%CE%B9+%CE%B1%CF%83%CE%BA%CE%AE%CF%83%CE%B5%CE%B9%CF%82+%CF%83%CF%84%CE%B1+%CE%B5%CE%BC%CE%B2%CE%B1%CE%B4%CE%AC+%CF%80%CE%BF%CE%BB%CF%85%CE%B3%CF%8E%CE%BD%CF%89%CE%BD&rft.jtitle=%5B%5B%CE%95%CF%85%CE%BA%CE%BB%CE%B5%CE%AF%CE%B4%CE%B7%CF%82+%CE%92%CE%84%5D%5D&rft.date=1977&rft.issue=2&rft.pages=28-30&rft_id=http%3A%2F%2Fniobe.hms.gr%2Fapothema%2F%3Fs%3Dsa%26i%3D2918&rfr_id=info:sid/el.wikipedia.org:%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD"><span style="display: none;"> </span></span></li> <li><span class="citation Journal">Κισκύρας Νίκος (1977). <a rel="nofollow" class="external text" href="http://niobe.hms.gr/apothema/?s=sa&i=2921">«Η μέθοδος των εμβαδών και η μέθοδος των όγκων»</a>. <i><a href="/wiki/%CE%95%CF%85%CE%BA%CE%BB%CE%B5%CE%AF%CE%B4%CE%B7%CF%82_%CE%92%CE%84" title="Ευκλείδης Β΄">Ευκλείδης Β΄</a></i> (2): 39-46<span class="printonly">. <a rel="nofollow" class="external free" href="http://niobe.hms.gr/apothema/?s=sa&i=2921">http://niobe.hms.gr/apothema/?s=sa&i=2921</a></span>.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=%CE%97+%CE%BC%CE%AD%CE%B8%CE%BF%CE%B4%CE%BF%CF%82+%CF%84%CF%89%CE%BD+%CE%B5%CE%BC%CE%B2%CE%B1%CE%B4%CF%8E%CE%BD+%CE%BA%CE%B1%CE%B9+%CE%B7+%CE%BC%CE%AD%CE%B8%CE%BF%CE%B4%CE%BF%CF%82+%CF%84%CF%89%CE%BD+%CF%8C%CE%B3%CE%BA%CF%89%CE%BD&rft.jtitle=%5B%5B%CE%95%CF%85%CE%BA%CE%BB%CE%B5%CE%AF%CE%B4%CE%B7%CF%82+%CE%92%CE%84%5D%5D&rft.aulast=%CE%9A%CE%B9%CF%83%CE%BA%CF%8D%CF%81%CE%B1%CF%82+%CE%9D%CE%AF%CE%BA%CE%BF%CF%82&rft.au=%CE%9A%CE%B9%CF%83%CE%BA%CF%8D%CF%81%CE%B1%CF%82+%CE%9D%CE%AF%CE%BA%CE%BF%CF%82&rft.date=1977&rft.issue=2&rft.pages=39-46&rft_id=http%3A%2F%2Fniobe.hms.gr%2Fapothema%2F%3Fs%3Dsa%26i%3D2921&rfr_id=info:sid/el.wikipedia.org:%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD"><span style="display: none;"> </span></span></li> <li><span class="citation Journal">Γ. Τασσόπουλος (1978). <a rel="nofollow" class="external text" href="http://niobe.hms.gr/apothema/?s=sa&i=4110">«Εμβαδό Κυρτού Πολυγώνου»</a>. <i><a href="/wiki/%CE%95%CF%85%CE%BA%CE%BB%CE%B5%CE%AF%CE%B4%CE%B7%CF%82_%CE%92%CE%84" title="Ευκλείδης Β΄">Ευκλείδης Β΄</a></i> (4): 155-157<span class="printonly">. <a rel="nofollow" class="external free" href="http://niobe.hms.gr/apothema/?s=sa&i=4110">http://niobe.hms.gr/apothema/?s=sa&i=4110</a></span>.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C+%CE%9A%CF%85%CF%81%CF%84%CE%BF%CF%8D+%CE%A0%CE%BF%CE%BB%CF%85%CE%B3%CF%8E%CE%BD%CE%BF%CF%85&rft.jtitle=%5B%5B%CE%95%CF%85%CE%BA%CE%BB%CE%B5%CE%AF%CE%B4%CE%B7%CF%82+%CE%92%CE%84%5D%5D&rft.aulast=%CE%93.+%CE%A4%CE%B1%CF%83%CF%83%CF%8C%CF%80%CE%BF%CF%85%CE%BB%CE%BF%CF%82&rft.au=%CE%93.+%CE%A4%CE%B1%CF%83%CF%83%CF%8C%CF%80%CE%BF%CF%85%CE%BB%CE%BF%CF%82&rft.date=1978&rft.issue=4&rft.pages=155-157&rft_id=http%3A%2F%2Fniobe.hms.gr%2Fapothema%2F%3Fs%3Dsa%26i%3D4110&rfr_id=info:sid/el.wikipedia.org:%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD"><span style="display: none;"> </span></span></li> <li><span class="citation Journal">Γιαννέλος, Δρακόπουλος (1980). <a rel="nofollow" class="external text" href="http://niobe.hms.gr/apothema/?s=sa&i=3951">«Εμβαδά ευθυγράμμων σχημάτων»</a>. <i><a href="/wiki/%CE%95%CF%85%CE%BA%CE%BB%CE%B5%CE%AF%CE%B4%CE%B7%CF%82_%CE%92%CE%84" title="Ευκλείδης Β΄">Ευκλείδης Β΄</a></i> (3): 24-26<span class="printonly">. <a rel="nofollow" class="external free" href="http://niobe.hms.gr/apothema/?s=sa&i=3951">http://niobe.hms.gr/apothema/?s=sa&i=3951</a></span>.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CE%AC+%CE%B5%CF%85%CE%B8%CF%85%CE%B3%CF%81%CE%AC%CE%BC%CE%BC%CF%89%CE%BD+%CF%83%CF%87%CE%B7%CE%BC%CE%AC%CF%84%CF%89%CE%BD&rft.jtitle=%5B%5B%CE%95%CF%85%CE%BA%CE%BB%CE%B5%CE%AF%CE%B4%CE%B7%CF%82+%CE%92%CE%84%5D%5D&rft.aulast=%CE%93%CE%B9%CE%B1%CE%BD%CE%BD%CE%AD%CE%BB%CE%BF%CF%82%2C+%CE%94%CF%81%CE%B1%CE%BA%CF%8C%CF%80%CE%BF%CF%85%CE%BB%CE%BF%CF%82&rft.au=%CE%93%CE%B9%CE%B1%CE%BD%CE%BD%CE%AD%CE%BB%CE%BF%CF%82%2C+%CE%94%CF%81%CE%B1%CE%BA%CF%8C%CF%80%CE%BF%CF%85%CE%BB%CE%BF%CF%82&rft.date=1980&rft.issue=3&rft.pages=24-26&rft_id=http%3A%2F%2Fniobe.hms.gr%2Fapothema%2F%3Fs%3Dsa%26i%3D3951&rfr_id=info:sid/el.wikipedia.org:%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD"><span style="display: none;"> </span></span></li> <li><span class="citation Journal">Χ. Παπαδόπουλος (1981). <a rel="nofollow" class="external text" href="http://niobe.hms.gr/apothema/?s=sa&i=2718">«Εμβαδό τριγώνου»</a>. <i><a href="/wiki/%CE%95%CF%85%CE%BA%CE%BB%CE%B5%CE%AF%CE%B4%CE%B7%CF%82_%CE%92%CE%84" title="Ευκλείδης Β΄">Ευκλείδης Β΄</a></i> (1): 49-51<span class="printonly">. <a rel="nofollow" class="external free" href="http://niobe.hms.gr/apothema/?s=sa&i=2718">http://niobe.hms.gr/apothema/?s=sa&i=2718</a></span>.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C+%CF%84%CF%81%CE%B9%CE%B3%CF%8E%CE%BD%CE%BF%CF%85&rft.jtitle=%5B%5B%CE%95%CF%85%CE%BA%CE%BB%CE%B5%CE%AF%CE%B4%CE%B7%CF%82+%CE%92%CE%84%5D%5D&rft.aulast=%CE%A7.+%CE%A0%CE%B1%CF%80%CE%B1%CE%B4%CF%8C%CF%80%CE%BF%CF%85%CE%BB%CE%BF%CF%82&rft.au=%CE%A7.+%CE%A0%CE%B1%CF%80%CE%B1%CE%B4%CF%8C%CF%80%CE%BF%CF%85%CE%BB%CE%BF%CF%82&rft.date=1981&rft.issue=1&rft.pages=49-51&rft_id=http%3A%2F%2Fniobe.hms.gr%2Fapothema%2F%3Fs%3Dsa%26i%3D2718&rfr_id=info:sid/el.wikipedia.org:%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD"><span style="display: none;"> </span></span></li> <li><span class="citation Journal">Β. Γιαννακόπουλος (1983). <a rel="nofollow" class="external text" href="http://niobe.hms.gr/apothema/?s=sa&i=3149">«Μια σημείωση στα εμβαδά, στα κανονικά πολύγωνα και στον κύκλο»</a>. <i><a href="/wiki/%CE%95%CF%85%CE%BA%CE%BB%CE%B5%CE%AF%CE%B4%CE%B7%CF%82_%CE%92%CE%84" title="Ευκλείδης Β΄">Ευκλείδης Β΄</a></i> (3): 201-204<span class="printonly">. <a rel="nofollow" class="external free" href="http://niobe.hms.gr/apothema/?s=sa&i=3149">http://niobe.hms.gr/apothema/?s=sa&i=3149</a></span>.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=%CE%9C%CE%B9%CE%B1+%CF%83%CE%B7%CE%BC%CE%B5%CE%AF%CF%89%CF%83%CE%B7+%CF%83%CF%84%CE%B1+%CE%B5%CE%BC%CE%B2%CE%B1%CE%B4%CE%AC%2C+%CF%83%CF%84%CE%B1+%CE%BA%CE%B1%CE%BD%CE%BF%CE%BD%CE%B9%CE%BA%CE%AC+%CF%80%CE%BF%CE%BB%CF%8D%CE%B3%CF%89%CE%BD%CE%B1+%CE%BA%CE%B1%CE%B9+%CF%83%CF%84%CE%BF%CE%BD+%CE%BA%CF%8D%CE%BA%CE%BB%CE%BF&rft.jtitle=%5B%5B%CE%95%CF%85%CE%BA%CE%BB%CE%B5%CE%AF%CE%B4%CE%B7%CF%82+%CE%92%CE%84%5D%5D&rft.aulast=%CE%92.+%CE%93%CE%B9%CE%B1%CE%BD%CE%BD%CE%B1%CE%BA%CF%8C%CF%80%CE%BF%CF%85%CE%BB%CE%BF%CF%82&rft.au=%CE%92.+%CE%93%CE%B9%CE%B1%CE%BD%CE%BD%CE%B1%CE%BA%CF%8C%CF%80%CE%BF%CF%85%CE%BB%CE%BF%CF%82&rft.date=1983&rft.issue=3&rft.pages=201-204&rft_id=http%3A%2F%2Fniobe.hms.gr%2Fapothema%2F%3Fs%3Dsa%26i%3D3149&rfr_id=info:sid/el.wikipedia.org:%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD"><span style="display: none;"> </span></span></li> <li><span class="citation Journal">Μ. Λεγάκης (1984). <a rel="nofollow" class="external text" href="http://niobe.hms.gr/apothema/?s=sa&i=3149">«Εμβαδά και Περίμετροι ευθυγράμμων Σχημάτων»</a>. <i><a href="/wiki/%CE%95%CF%85%CE%BA%CE%BB%CE%B5%CE%AF%CE%B4%CE%B7%CF%82_%CE%91%CE%84" title="Ευκλείδης Α΄">Ευκλείδης Α΄</a></i> (3): 201-204<span class="printonly">. <a rel="nofollow" class="external free" href="http://niobe.hms.gr/apothema/?s=sa&i=3149">http://niobe.hms.gr/apothema/?s=sa&i=3149</a></span>.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CE%AC+%CE%BA%CE%B1%CE%B9+%CE%A0%CE%B5%CF%81%CE%AF%CE%BC%CE%B5%CF%84%CF%81%CE%BF%CE%B9+%CE%B5%CF%85%CE%B8%CF%85%CE%B3%CF%81%CE%AC%CE%BC%CE%BC%CF%89%CE%BD+%CE%A3%CF%87%CE%B7%CE%BC%CE%AC%CF%84%CF%89%CE%BD&rft.jtitle=%5B%5B%CE%95%CF%85%CE%BA%CE%BB%CE%B5%CE%AF%CE%B4%CE%B7%CF%82+%CE%91%CE%84%5D%5D&rft.aulast=%CE%9C.+%CE%9B%CE%B5%CE%B3%CE%AC%CE%BA%CE%B7%CF%82&rft.au=%CE%9C.+%CE%9B%CE%B5%CE%B3%CE%AC%CE%BA%CE%B7%CF%82&rft.date=1984&rft.issue=3&rft.pages=201-204&rft_id=http%3A%2F%2Fniobe.hms.gr%2Fapothema%2F%3Fs%3Dsa%26i%3D3149&rfr_id=info:sid/el.wikipedia.org:%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD"><span style="display: none;"> </span></span></li> <li><span class="citation Journal">Δ. Λιουδάκης (1989). <a rel="nofollow" class="external text" href="http://niobe.hms.gr/apothema/?s=sa&i=3228">«Εμβαδά Επίπεδων Σχημάτων»</a>. <i><a href="/wiki/%CE%95%CF%85%CE%BA%CE%BB%CE%B5%CE%AF%CE%B4%CE%B7%CF%82_%CE%92%CE%84" title="Ευκλείδης Β΄">Ευκλείδης Β΄</a></i> (3): 25-28<span class="printonly">. <a rel="nofollow" class="external free" href="http://niobe.hms.gr/apothema/?s=sa&i=3228">http://niobe.hms.gr/apothema/?s=sa&i=3228</a></span>.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CE%AC+%CE%95%CF%80%CE%AF%CF%80%CE%B5%CE%B4%CF%89%CE%BD+%CE%A3%CF%87%CE%B7%CE%BC%CE%AC%CF%84%CF%89%CE%BD&rft.jtitle=%5B%5B%CE%95%CF%85%CE%BA%CE%BB%CE%B5%CE%AF%CE%B4%CE%B7%CF%82+%CE%92%CE%84%5D%5D&rft.aulast=%CE%94.+%CE%9B%CE%B9%CE%BF%CF%85%CE%B4%CE%AC%CE%BA%CE%B7%CF%82&rft.au=%CE%94.+%CE%9B%CE%B9%CE%BF%CF%85%CE%B4%CE%AC%CE%BA%CE%B7%CF%82&rft.date=1989&rft.issue=3&rft.pages=25-28&rft_id=http%3A%2F%2Fniobe.hms.gr%2Fapothema%2F%3Fs%3Dsa%26i%3D3228&rfr_id=info:sid/el.wikipedia.org:%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD"><span style="display: none;"> </span></span></li> <li><span class="citation Journal">Γκαμψάλα Χρύσα (1990). <a rel="nofollow" class="external text" href="http://niobe.hms.gr/apothema/?s=sa&i=3403">«Τα εμβαδά των επίπεδων χώρων»</a>. <i><a href="/wiki/%CE%95%CF%85%CE%BA%CE%BB%CE%B5%CE%AF%CE%B4%CE%B7%CF%82_%CE%92%CE%84" title="Ευκλείδης Β΄">Ευκλείδης Β΄</a></i> (4): 30-34<span class="printonly">. <a rel="nofollow" class="external free" href="http://niobe.hms.gr/apothema/?s=sa&i=3403">http://niobe.hms.gr/apothema/?s=sa&i=3403</a></span>.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=%CE%A4%CE%B1+%CE%B5%CE%BC%CE%B2%CE%B1%CE%B4%CE%AC+%CF%84%CF%89%CE%BD+%CE%B5%CF%80%CE%AF%CF%80%CE%B5%CE%B4%CF%89%CE%BD+%CF%87%CF%8E%CF%81%CF%89%CE%BD&rft.jtitle=%5B%5B%CE%95%CF%85%CE%BA%CE%BB%CE%B5%CE%AF%CE%B4%CE%B7%CF%82+%CE%92%CE%84%5D%5D&rft.aulast=%CE%93%CE%BA%CE%B1%CE%BC%CF%88%CE%AC%CE%BB%CE%B1+%CE%A7%CF%81%CF%8D%CF%83%CE%B1&rft.au=%CE%93%CE%BA%CE%B1%CE%BC%CF%88%CE%AC%CE%BB%CE%B1+%CE%A7%CF%81%CF%8D%CF%83%CE%B1&rft.date=1990&rft.issue=4&rft.pages=30-34&rft_id=http%3A%2F%2Fniobe.hms.gr%2Fapothema%2F%3Fs%3Dsa%26i%3D3403&rfr_id=info:sid/el.wikipedia.org:%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD"><span style="display: none;"> </span></span></li></ul> <div class="mw-heading mw-heading3"><h3 id="Ξενόγλωσσα_άρθρα"><span id=".CE.9E.CE.B5.CE.BD.CF.8C.CE.B3.CE.BB.CF.89.CF.83.CF.83.CE.B1_.CE.AC.CF.81.CE.B8.CF.81.CE.B1"></span>Ξενόγλωσσα άρθρα</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&veaction=edit&section=18" title="Επεξεργασία ενότητας: Ξενόγλωσσα άρθρα" class="mw-editsection-visualeditor"><span>Επεξεργασία</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&action=edit&section=18" title="Επεξεργαστείτε τον πηγαίο κώδικα της ενότητας: Ξενόγλωσσα άρθρα"><span>επεξεργασία κώδικα</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="citation Journal">Trainin, J. (2007). <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/40378436">«91.70 an Elementary Proof of Pick's Theorem»</a>. <i>The Mathematical Gazette</i> <b>91</b> (522): 536-540<span class="printonly">. <a rel="nofollow" class="external free" href="https://www.jstor.org/stable/40378436">https://www.jstor.org/stable/40378436</a></span>.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=91.70+an+Elementary+Proof+of+Pick%27s+Theorem&rft.jtitle=The+Mathematical+Gazette&rft.aulast=Trainin&rft.aufirst=J.&rft.au=Trainin%2C%26%2332%3BJ.&rft.date=2007&rft.volume=91&rft.issue=522&rft.pages=536-540&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F40378436&rfr_id=info:sid/el.wikipedia.org:%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD"><span style="display: none;"> </span></span></li> <li><span class="citation Journal">Stein, Sherman (Δεκεμβρίου 2004). «Cutting a Polygon into Triangles of Equal Areas». <i>The Mathematical Intelligencer</i> <b>26</b> (1): 17–21. <a href="/wiki/Digital_object_identifier" class="mw-redirect" title="Digital object identifier">doi</a>:<span class="neverexpand"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.1007%2FBF02985395">10.1007/BF02985395</a></span>.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Cutting+a+Polygon+into+Triangles+of+Equal+Areas&rft.jtitle=The+Mathematical+Intelligencer&rft.aulast=Stein&rft.aufirst=Sherman&rft.au=Stein%2C%26%2332%3BSherman&rft.date=%CE%94%CE%B5%CE%BA%CE%B5%CE%BC%CE%B2%CF%81%CE%AF%CE%BF%CF%85+2004&rft.volume=26&rft.issue=1&rft.pages=17%E2%80%9321&rft_id=info:doi/10.1007%2FBF02985395&rfr_id=info:sid/el.wikipedia.org:%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD"><span style="display: none;"> </span></span></li> <li><span class="citation Journal">Di Domenico, Angelo S. (Ιουλίου 2003). <a rel="nofollow" class="external text" href="https://archive.org/details/sim_mathematical-gazette_2003-07_87_509/page/323">«87.46 A property of triangles involving area»</a>. <i>The Mathematical Gazette</i> <b>87</b> (509): 323–324. <a href="/wiki/Digital_object_identifier" class="mw-redirect" title="Digital object identifier">doi</a>:<span class="neverexpand"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.1017%2FS0025557200172870">10.1017/S0025557200172870</a></span><span class="printonly">. <a rel="nofollow" class="external free" href="https://archive.org/details/sim_mathematical-gazette_2003-07_87_509/page/323">https://archive.org/details/sim_mathematical-gazette_2003-07_87_509/page/323</a></span>.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=87.46+A+property+of+triangles+involving+area&rft.jtitle=The+Mathematical+Gazette&rft.aulast=Di+Domenico&rft.aufirst=Angelo+S.&rft.au=Di+Domenico%2C%26%2332%3BAngelo+S.&rft.date=%CE%99%CE%BF%CF%85%CE%BB%CE%AF%CE%BF%CF%85+2003&rft.volume=87&rft.issue=509&rft.pages=323%E2%80%93324&rft_id=info:doi/10.1017%2FS0025557200172870&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fsim_mathematical-gazette_2003-07_87_509%2Fpage%2F323&rfr_id=info:sid/el.wikipedia.org:%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD"><span style="display: none;"> </span></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="Παραπομπές"><span id=".CE.A0.CE.B1.CF.81.CE.B1.CF.80.CE.BF.CE.BC.CF.80.CE.AD.CF.82"></span>Παραπομπές</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&veaction=edit&section=19" title="Επεξεργασία ενότητας: Παραπομπές" class="mw-editsection-visualeditor"><span>Επεξεργασία</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD&action=edit&section=19" title="Επεξεργαστείτε τον πηγαίο κώδικα της ενότητας: Παραπομπές"><span>επεξεργασία κώδικα</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-Tav-1"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-Tav_1-0">1,0</a></sup> <sup><a href="#cite_ref-Tav_1-1">1,1</a></sup> <sup><a href="#cite_ref-Tav_1-2">1,2</a></sup> <sup><a href="#cite_ref-Tav_1-3">1,3</a></sup> <sup><a href="#cite_ref-Tav_1-4">1,4</a></sup></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r9162355">.mw-parser-output cite.citation{font-style:inherit}.mw-parser-output q{quotes:"«""»""\"""\"""'""'"}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:inherit;padding:inherit}.mw-parser-output .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-lock-limited a,.mw-parser-output .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}</style><cite class="citation book">Ταβανλης, Χ. <i>Επίπεδος Γεωμετρία</i>. Αθήνα: Ι. Χιωτελη.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%CE%95%CF%80%CE%AF%CF%80%CE%B5%CE%B4%CE%BF%CF%82+%CE%93%CE%B5%CF%89%CE%BC%CE%B5%CF%84%CF%81%CE%AF%CE%B1&rft.place=%CE%91%CE%B8%CE%AE%CE%BD%CE%B1&rft.pub=%CE%99.+%CE%A7%CE%B9%CF%89%CF%84%CE%B5%CE%BB%CE%B7&rft.aulast=%CE%A4%CE%B1%CE%B2%CE%B1%CE%BD%CE%BB%CE%B7%CF%82&rft.aufirst=%CE%A7.&rfr_id=info%3Asid%2Fel.wikipedia.org%3A%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r9162355" /><cite class="citation book">Στεργίου, Μπάμπης. <i>Γεωμετρία για διαγωνισμούς 2: Μετρικές σχέσεις σε τρίγωνα, Πολύγωνα, Εμβαδά</i>. Αθήνα: Σαββάλας. <a href="/wiki/%CE%94%CE%B9%CE%B5%CE%B8%CE%BD%CE%AE%CF%82_%CF%80%CF%81%CF%8C%CF%84%CF%85%CF%80%CE%BF%CF%82_%CE%B1%CF%81%CE%B9%CE%B8%CE%BC%CF%8C%CF%82_%CE%B2%CE%B9%CE%B2%CE%BB%CE%AF%CE%BF%CF%85" title="Διεθνής πρότυπος αριθμός βιβλίου">ISBN</a> <a href="/wiki/%CE%95%CE%B9%CE%B4%CE%B9%CE%BA%CF%8C:%CE%A0%CE%B7%CE%B3%CE%AD%CF%82%CE%92%CE%B9%CE%B2%CE%BB%CE%AF%CF%89%CE%BD/978-960-493-159-0" title="Ειδικό:ΠηγέςΒιβλίων/978-960-493-159-0">978-960-493-159-0</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%CE%93%CE%B5%CF%89%CE%BC%CE%B5%CF%84%CF%81%CE%AF%CE%B1+%CE%B3%CE%B9%CE%B1+%CE%B4%CE%B9%CE%B1%CE%B3%CF%89%CE%BD%CE%B9%CF%83%CE%BC%CE%BF%CF%8D%CF%82+2%3A+%CE%9C%CE%B5%CF%84%CF%81%CE%B9%CE%BA%CE%AD%CF%82+%CF%83%CF%87%CE%AD%CF%83%CE%B5%CE%B9%CF%82+%CF%83%CE%B5+%CF%84%CF%81%CE%AF%CE%B3%CF%89%CE%BD%CE%B1%2C+%CE%A0%CE%BF%CE%BB%CF%8D%CE%B3%CF%89%CE%BD%CE%B1%2C+%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CE%AC&rft.place=%CE%91%CE%B8%CE%AE%CE%BD%CE%B1&rft.pub=%CE%A3%CE%B1%CE%B2%CE%B2%CE%AC%CE%BB%CE%B1%CF%82&rft.isbn=978-960-493-159-0&rft.aulast=%CE%A3%CF%84%CE%B5%CF%81%CE%B3%CE%AF%CE%BF%CF%85&rft.aufirst=%CE%9C%CF%80%CE%AC%CE%BC%CF%80%CE%B7%CF%82&rfr_id=info%3Asid%2Fel.wikipedia.org%3A%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-T57-3"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-T57_3-0">3,00</a></sup> <sup><a href="#cite_ref-T57_3-1">3,01</a></sup> <sup><a href="#cite_ref-T57_3-2">3,02</a></sup> <sup><a href="#cite_ref-T57_3-3">3,03</a></sup> <sup><a href="#cite_ref-T57_3-4">3,04</a></sup> <sup><a href="#cite_ref-T57_3-5">3,05</a></sup> <sup><a href="#cite_ref-T57_3-6">3,06</a></sup> <sup><a href="#cite_ref-T57_3-7">3,07</a></sup> <sup><a href="#cite_ref-T57_3-8">3,08</a></sup> <sup><a href="#cite_ref-T57_3-9">3,09</a></sup> <sup><a href="#cite_ref-T57_3-10">3,10</a></sup> <sup><a href="#cite_ref-T57_3-11">3,11</a></sup> <sup><a href="#cite_ref-T57_3-12">3,12</a></sup> <sup><a href="#cite_ref-T57_3-13">3,13</a></sup> <sup><a href="#cite_ref-T57_3-14">3,14</a></sup> <sup><a href="#cite_ref-T57_3-15">3,15</a></sup> <sup><a href="#cite_ref-T57_3-16">3,16</a></sup> <sup><a href="#cite_ref-T57_3-17">3,17</a></sup> <sup><a href="#cite_ref-T57_3-18">3,18</a></sup></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r9162355" /><cite class="citation book">Τόγκας, Πέτρος Γ. (1957). <i>Θεωρητική Γεωμετρία</i>. Αθήνα: Πέτρου Γ. Τόγκα.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%CE%98%CE%B5%CF%89%CF%81%CE%B7%CF%84%CE%B9%CE%BA%CE%AE+%CE%93%CE%B5%CF%89%CE%BC%CE%B5%CF%84%CF%81%CE%AF%CE%B1&rft.place=%CE%91%CE%B8%CE%AE%CE%BD%CE%B1&rft.pub=%CE%A0%CE%AD%CF%84%CF%81%CE%BF%CF%85+%CE%93.+%CE%A4%CF%8C%CE%B3%CE%BA%CE%B1&rft.date=1957&rft.aulast=%CE%A4%CF%8C%CE%B3%CE%BA%CE%B1%CF%82&rft.aufirst=%CE%A0%CE%AD%CF%84%CF%81%CE%BF%CF%82+%CE%93.&rfr_id=info%3Asid%2Fel.wikipedia.org%3A%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r9162355" /><cite class="citation book">Andreescu, Titu· Dorin, Andrica (2006). <a rel="nofollow" class="external text" href="https://archive.org/details/complexnumbersfr0000andr"><i>Complex numbers from A to ... Z</i></a>. Boston Basel Berlin: Birkhäuser. <a href="/wiki/%CE%94%CE%B9%CE%B5%CE%B8%CE%BD%CE%AE%CF%82_%CF%80%CF%81%CF%8C%CF%84%CF%85%CF%80%CE%BF%CF%82_%CE%B1%CF%81%CE%B9%CE%B8%CE%BC%CF%8C%CF%82_%CE%B2%CE%B9%CE%B2%CE%BB%CE%AF%CE%BF%CF%85" title="Διεθνής πρότυπος αριθμός βιβλίου">ISBN</a> <a href="/wiki/%CE%95%CE%B9%CE%B4%CE%B9%CE%BA%CF%8C:%CE%A0%CE%B7%CE%B3%CE%AD%CF%82%CE%92%CE%B9%CE%B2%CE%BB%CE%AF%CF%89%CE%BD/9780817643263" title="Ειδικό:ΠηγέςΒιβλίων/9780817643263">9780817643263</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Complex+numbers+from+A+to+...+Z&rft.place=Boston+Basel+Berlin&rft.pub=Birkh%C3%A4user&rft.date=2006&rft.isbn=9780817643263&rft.aulast=Andreescu&rft.aufirst=Titu&rft.au=Dorin%2C+Andrica&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fcomplexnumbersfr0000andr&rfr_id=info%3Asid%2Fel.wikipedia.org%3A%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD" class="Z3988"><span style="display:none;"> </span></span></span> </li> </ol></div> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r10387572">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output 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