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class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Retejo"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Enhavo" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc 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">Enhavo</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">movigi al flanka panelo</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">kaŝi</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">Komenco</div> </a> </li> <li id="toc-Difinoj" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Difinoj"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Difinoj</span> </div> </a> <ul id="toc-Difinoj-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Historio" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Historio"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Historio</span> </div> </a> <ul id="toc-Historio-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Area_de_ebenaj_figuroj" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Area_de_ebenaj_figuroj"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Area de ebenaj figuroj</span> </div> </a> <button aria-controls="toc-Area_de_ebenaj_figuroj-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>Baskuli Area de ebenaj figuroj subsekcio</span> </button> <ul id="toc-Area_de_ebenaj_figuroj-sublist" class="vector-toc-list"> <li id="toc-Areo_de_triangulo" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Areo_de_triangulo"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Areo de triangulo</span> </div> </a> <ul id="toc-Areo_de_triangulo-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Area_de_kvarlatero" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Area_de_kvarlatero"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Area de kvarlatero</span> </div> </a> <ul id="toc-Area_de_kvarlatero-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Areo_de_la_disko_kaj_de_la_elipso" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Areo_de_la_disko_kaj_de_la_elipso"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Areo de la disko kaj de la elipso</span> </div> </a> <ul id="toc-Areo_de_la_disko_kaj_de_la_elipso-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Areo_limigita_inter_du_funkcioj" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Areo_limigita_inter_du_funkcioj"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Areo limigita inter du funkcioj</span> </div> </a> <ul id="toc-Areo_limigita_inter_du_funkcioj-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Rilato_areo-perimetro" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Rilato_areo-perimetro"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.5</span> <span>Rilato areo-perimetro</span> </div> </a> <ul id="toc-Rilato_areo-perimetro-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Disvastiĝa_areo" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Disvastiĝa_areo"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Disvastiĝa areo</span> </div> </a> <ul id="toc-Disvastiĝa_areo-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bildaro" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bildaro"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Bildaro</span> </div> </a> <ul id="toc-Bildaro-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Referencoj" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Referencoj"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Referencoj</span> </div> </a> <ul id="toc-Referencoj-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Literaturo" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Literaturo"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Literaturo</span> </div> </a> <ul id="toc-Literaturo-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Eksteraj_ligiloj" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Eksteraj_ligiloj"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Eksteraj ligiloj</span> </div> </a> <ul id="toc-Eksteraj_ligiloj-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="Enhavo" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Enhavtabelo" > <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="Ŝaltu la enhavtabelon" > <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">Ŝaltu la enhavtabelon</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">Areo</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="Iru al artikolo en alia lingvo. Havebla en 165 lingvo" > <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 lingvoj</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 — afrikansa" lang="af" hreflang="af" data-title="Oppervlakte" data-language-autonym="Afrikaans" data-language-local-name="afrikansa" 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 — svisgermana" lang="gsw" hreflang="gsw" data-title="Flächeninhalt" data-language-autonym="Alemannisch" data-language-local-name="svisgermana" 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 — aragona" lang="an" hreflang="an" data-title="Aria" data-language-autonym="Aragonés" data-language-local-name="aragona" 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 — angika" lang="anp" hreflang="anp" data-title="क्षेत्रफल" data-language-autonym="अंगिका" data-language-local-name="angika" 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 — araba" lang="ar" hreflang="ar" data-title="مساحة" data-language-autonym="العربية" data-language-local-name="araba" 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 — Aramaic" lang="arc" hreflang="arc" data-title="ܫܛܝܚܘܬܐ" data-language-autonym="ܐܪܡܝܐ" data-language-local-name="Aramaic" 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 — asama" lang="as" hreflang="as" data-title="ক্ষেত্ৰফল" data-language-autonym="অসমীয়া" data-language-local-name="asama" 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) — astura" lang="ast" hreflang="ast" data-title="Área (xeometría)" data-language-autonym="Asturianu" data-language-local-name="astura" 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 — avara" lang="av" hreflang="av" data-title="Площадь" data-language-autonym="Авар" data-language-local-name="avara" 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 — avadhia" lang="awa" hreflang="awa" data-title="क्षेत्रफल" data-language-autonym="अवधी" data-language-local-name="avadhia" 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) — azerbajĝana" lang="az" hreflang="az" data-title="Sahə (ölçü parametri)" data-language-autonym="Azərbaycanca" data-language-local-name="azerbajĝana" 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 — baŝkira" lang="ba" hreflang="ba" data-title="Майҙан" data-language-autonym="Башҡортса" data-language-local-name="baŝkira" 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 — belorusa" lang="be" hreflang="be" data-title="Плошча" data-language-autonym="Беларуская" data-language-local-name="belorusa" 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 — bulgara" lang="bg" hreflang="bg" data-title="Площ" data-language-autonym="Български" data-language-local-name="bulgara" 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 — bengala" lang="bn" hreflang="bn" data-title="ক্ষেত্রফল" data-language-autonym="বাংলা" data-language-local-name="bengala" 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 — bretona" lang="br" hreflang="br" data-title="Gorread" data-language-autonym="Brezhoneg" data-language-local-name="bretona" 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 — bosna" lang="bs" hreflang="bs" data-title="Površina" data-language-autonym="Bosanski" data-language-local-name="bosna" 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 — kataluna" lang="ca" hreflang="ca" data-title="Àrea" data-language-autonym="Català" data-language-local-name="kataluna" 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 — ĉeĉena" lang="ce" hreflang="ce" data-title="Майда" data-language-autonym="Нохчийн" data-language-local-name="ĉeĉena" 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 — cebua" lang="ceb" hreflang="ceb" data-title="Langyab" data-language-autonym="Cebuano" data-language-local-name="cebua" 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 — sorana" lang="ckb" hreflang="ckb" data-title="ڕووبەر" data-language-autonym="کوردی" data-language-local-name="sorana" 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 — ĉeĥa" lang="cs" hreflang="cs" data-title="Obsah" data-language-autonym="Čeština" data-language-local-name="ĉeĥa" 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 — malnovslava" lang="cu" hreflang="cu" data-title="Пространиѥ" data-language-autonym="Словѣньскъ / ⰔⰎⰑⰂⰡⰐⰠⰔⰍⰟ" data-language-local-name="malnovslava" 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 — ĉuvaŝa" lang="cv" hreflang="cv" data-title="Лаптăк" data-language-autonym="Чӑвашла" data-language-local-name="ĉuvaŝa" 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 — kimra" lang="cy" hreflang="cy" data-title="Arwynebedd" data-language-autonym="Cymraeg" data-language-local-name="kimra" 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 — dana" lang="da" hreflang="da" data-title="Areal" data-language-autonym="Dansk" data-language-local-name="dana" 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 — germana" lang="de" hreflang="de" data-title="Flächeninhalt" data-language-autonym="Deutsch" data-language-local-name="germana" 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 — malsuprasoraba" lang="dsb" hreflang="dsb" data-title="Wopśimjeśe płoni" data-language-autonym="Dolnoserbski" data-language-local-name="malsuprasoraba" 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 — maldiva" lang="dv" hreflang="dv" data-title="އަކަމިން" data-language-autonym="ދިވެހިބަސް" data-language-local-name="maldiva" class="interlanguage-link-target"><span>ދިވެހިބަސް</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD" title="Εμβαδόν — greka" lang="el" hreflang="el" data-title="Εμβαδόν" data-language-autonym="Ελληνικά" data-language-local-name="greka" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Area" title="Area — angla" lang="en" hreflang="en" data-title="Area" data-language-autonym="English" data-language-local-name="angla" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/%C3%81rea" title="Área — hispana" lang="es" hreflang="es" data-title="Área" data-language-autonym="Español" data-language-local-name="hispana" 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 — estona" lang="et" hreflang="et" data-title="Pindala" data-language-autonym="Eesti" data-language-local-name="estona" 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 — eŭska" lang="eu" hreflang="eu" data-title="Azalera" data-language-autonym="Euskara" data-language-local-name="eŭska" 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 — persa" lang="fa" hreflang="fa" data-title="مساحت" data-language-autonym="فارسی" data-language-local-name="persa" 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 — finna" lang="fi" hreflang="fi" data-title="Pinta-ala" data-language-autonym="Suomi" data-language-local-name="finna" 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 — fiĝia" lang="fj" hreflang="fj" data-title="Iwasewase" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="fiĝia" 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 — feroa" lang="fo" hreflang="fo" data-title="Vídd" data-language-autonym="Føroyskt" data-language-local-name="feroa" 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) — franca" lang="fr" hreflang="fr" data-title="Aire (géométrie)" data-language-autonym="Français" data-language-local-name="franca" 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) — nord-frisa" lang="frr" hreflang="frr" data-title="Areaal (Miat)" data-language-autonym="Nordfriisk" data-language-local-name="nord-frisa" 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 — okcident-frisa" lang="fy" hreflang="fy" data-title="Oerflak" data-language-autonym="Frysk" data-language-local-name="okcident-frisa" 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 — skot-gaela" lang="gd" hreflang="gd" data-title="Farsaingeachd" data-language-autonym="Gàidhlig" data-language-local-name="skot-gaela" 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 — galega" lang="gl" hreflang="gl" data-title="Área" data-language-autonym="Galego" data-language-local-name="galega" 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 — gvarania" lang="gn" hreflang="gn" data-title="Tendaha" data-language-autonym="Avañe'ẽ" data-language-local-name="gvarania" 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 — guĝarata" lang="gu" hreflang="gu" data-title="ક્ષેત્રફળ" data-language-autonym="ગુજરાતી" data-language-local-name="guĝarata" 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 — manksa" lang="gv" hreflang="gv" data-title="Eaghtyr" data-language-autonym="Gaelg" data-language-local-name="manksa" 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 — havaja" lang="haw" hreflang="haw" data-title="ʻAlea" data-language-autonym="Hawaiʻi" data-language-local-name="havaja" 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 — hebrea" lang="he" hreflang="he" data-title="שטח" data-language-autonym="עברית" data-language-local-name="hebrea" 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 — hinda" lang="hi" hreflang="hi" data-title="क्षेत्रफल" data-language-autonym="हिन्दी" data-language-local-name="hinda" 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 — kroata" lang="hr" hreflang="hr" data-title="Površina" data-language-autonym="Hrvatski" data-language-local-name="kroata" 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 — suprasoraba" lang="hsb" hreflang="hsb" data-title="Wobsah přestrjenje" data-language-autonym="Hornjoserbsce" data-language-local-name="suprasoraba" 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) — hungara" lang="hu" hreflang="hu" data-title="Terület (matematika)" data-language-autonym="Magyar" data-language-local-name="hungara" 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 — armena" lang="hy" hreflang="hy" data-title="Մակերես" data-language-autonym="Հայերեն" data-language-local-name="armena" 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 — Interlingvao" lang="ia" hreflang="ia" data-title="Area" data-language-autonym="Interlingua" data-language-local-name="Interlingvao" 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 — indonezia" lang="id" hreflang="id" data-title="Luas" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonezia" 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 — iloka" lang="ilo" hreflang="ilo" data-title="Kalawa" data-language-autonym="Ilokano" data-language-local-name="iloka" 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 — Ido" lang="io" hreflang="io" data-title="Areo" data-language-autonym="Ido" data-language-local-name="Ido" 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 — islanda" lang="is" hreflang="is" data-title="Flatarmál" data-language-autonym="Íslenska" data-language-local-name="islanda" 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 — itala" lang="it" hreflang="it" data-title="Area" data-language-autonym="Italiano" data-language-local-name="itala" 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 — japana" lang="ja" hreflang="ja" data-title="面積" data-language-autonym="日本語" data-language-local-name="japana" 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 — java" lang="jv" hreflang="jv" data-title="Jembar" data-language-autonym="Jawa" data-language-local-name="java" 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 — kartvela" lang="ka" hreflang="ka" data-title="ფართობი" data-language-autonym="ქართული" data-language-local-name="kartvela" 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 — kabila" lang="kab" hreflang="kab" data-title="Tajumma" data-language-autonym="Taqbaylit" data-language-local-name="kabila" 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 — kabarda" lang="kbd" hreflang="kbd" data-title="ЩӀыпӀэ инагъ" data-language-autonym="Адыгэбзэ" data-language-local-name="kabarda" 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) — kazaĥa" lang="kk" hreflang="kk" data-title="Аудан (геометрия)" data-language-autonym="Қазақша" data-language-local-name="kazaĥa" 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 — kmera" lang="km" hreflang="km" data-title="ក្រលាផ្ទៃ" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="kmera" 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 — korea" lang="ko" hreflang="ko" data-title="넓이" data-language-autonym="한국어" data-language-local-name="korea" 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 — karaĉaj-balkara" lang="krc" hreflang="krc" data-title="Майданлыкъ" data-language-autonym="Къарачай-малкъар" data-language-local-name="karaĉaj-balkara" 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 — kurda" lang="ku" hreflang="ku" data-title="Rûerd" data-language-autonym="Kurdî" data-language-local-name="kurda" 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) — kornvala" lang="kw" hreflang="kw" data-title="Enep (fysegieth)" data-language-autonym="Kernowek" data-language-local-name="kornvala" 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 — kirgiza" lang="ky" hreflang="ky" data-title="Аянт" data-language-autonym="Кыргызча" data-language-local-name="kirgiza" 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) — latino" lang="la" hreflang="la" data-title="Area (geometria)" data-language-autonym="Latina" data-language-local-name="latino" 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 — luksemburga" lang="lb" hreflang="lb" data-title="Fläch" data-language-autonym="Lëtzebuergesch" data-language-local-name="luksemburga" 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 — limburga" lang="li" hreflang="li" data-title="Oppervlak" data-language-autonym="Limburgs" data-language-local-name="limburga" 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 — ligura" lang="lij" hreflang="lij" data-title="Area" data-language-autonym="Ligure" data-language-local-name="ligura" 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 — lombarda" lang="lmo" hreflang="lmo" data-title="Area" data-language-autonym="Lombard" data-language-local-name="lombarda" 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 — lingala" lang="ln" hreflang="ln" data-title="Etando" data-language-autonym="Lingála" data-language-local-name="lingala" 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 — laŭa" lang="lo" hreflang="lo" data-title="ເນື້ອທີ່" data-language-autonym="ລາວ" data-language-local-name="laŭa" 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 — litova" lang="lt" hreflang="lt" data-title="Plotas" data-language-autonym="Lietuvių" data-language-local-name="litova" 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 — latva" lang="lv" hreflang="lv" data-title="Laukums" data-language-autonym="Latviešu" data-language-local-name="latva" 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 — majtila" lang="mai" hreflang="mai" data-title="क्षेत्रफल" data-language-autonym="मैथिली" data-language-local-name="majtila" 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) — malagasa" lang="mg" hreflang="mg" data-title="Velarana (jeômetria)" data-language-autonym="Malagasy" data-language-local-name="malagasa" 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 — makedona" lang="mk" hreflang="mk" data-title="Плоштина" data-language-autonym="Македонски" data-language-local-name="makedona" 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 — malajalama" lang="ml" hreflang="ml" data-title="വിസ്തീർണ്ണം" data-language-autonym="മലയാളം" data-language-local-name="malajalama" 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 — mongola" lang="mn" hreflang="mn" data-title="Талбай" data-language-autonym="Монгол" data-language-local-name="mongola" 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 — manipura" lang="mni" hreflang="mni" data-title="ꯄꯥꯛꯆꯥꯎꯕ" data-language-autonym="ꯃꯤꯇꯩ ꯂꯣꯟ" data-language-local-name="manipura" 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 — marata" lang="mr" hreflang="mr" data-title="क्षेत्रफळ" data-language-autonym="मराठी" data-language-local-name="marata" 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 — malaja" lang="ms" hreflang="ms" data-title="Luas" data-language-autonym="Bahasa Melayu" data-language-local-name="malaja" 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 — miranda" lang="mwl" hreflang="mwl" data-title="Ária" data-language-autonym="Mirandés" data-language-local-name="miranda" 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 — birma" lang="my" hreflang="my" data-title="ဧရိယာ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="birma" 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 — mazandarana" lang="mzn" hreflang="mzn" data-title="گتی" data-language-autonym="مازِرونی" data-language-local-name="mazandarana" 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 — platgermana" lang="nds" hreflang="nds" data-title="Flach" data-language-autonym="Plattdüütsch" data-language-local-name="platgermana" 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 — Low Saxon" lang="nds-NL" hreflang="nds-NL" data-title="Oppervlakte" data-language-autonym="Nedersaksies" data-language-local-name="Low Saxon" 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 — nepala" lang="ne" hreflang="ne" data-title="क्षेत्रफल" data-language-autonym="नेपाली" data-language-local-name="nepala" 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 — nederlanda" lang="nl" hreflang="nl" data-title="Oppervlakte" data-language-autonym="Nederlands" data-language-local-name="nederlanda" 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 — novnorvega" lang="nn" hreflang="nn" data-title="Flatevidd" data-language-autonym="Norsk nynorsk" data-language-local-name="novnorvega" 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 — dannorvega" lang="nb" hreflang="nb" data-title="Areal" data-language-autonym="Norsk bokmål" data-language-local-name="dannorvega" 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 — okcitana" lang="oc" hreflang="oc" data-title="Aira" data-language-autonym="Occitan" data-language-local-name="okcitana" 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 — oseta" lang="os" hreflang="os" data-title="Фæзуат" data-language-autonym="Ирон" data-language-local-name="oseta" 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 — panĝaba" lang="pa" hreflang="pa" data-title="ਖੇਤਰਫਲ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="panĝaba" 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 — pola" lang="pl" hreflang="pl" data-title="Pole powierzchni" data-language-autonym="Polski" data-language-local-name="pola" 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 — portugala" lang="pt" hreflang="pt" data-title="Área" data-language-autonym="Português" data-language-local-name="portugala" 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 — keĉua" lang="qu" hreflang="qu" data-title="Hallka k'iti k'anchar" data-language-autonym="Runa Simi" data-language-local-name="keĉua" 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 — rumana" lang="ro" hreflang="ro" data-title="Arie" data-language-autonym="Română" data-language-local-name="rumana" 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 — rusa" lang="ru" hreflang="ru" data-title="Площадь" data-language-autonym="Русский" data-language-local-name="rusa" 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 — sanskrito" lang="sa" hreflang="sa" data-title="क्षेत्रफलम्" data-language-autonym="संस्कृतम्" data-language-local-name="sanskrito" 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 — jakuta" lang="sah" hreflang="sah" data-title="Иэн" data-language-autonym="Саха тыла" data-language-local-name="jakuta" 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) — sicilia" lang="scn" hreflang="scn" data-title="Ària (supirfici)" data-language-autonym="Sicilianu" data-language-local-name="sicilia" 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 — skota" lang="sco" hreflang="sco" data-title="Area" data-language-autonym="Scots" data-language-local-name="skota" 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 — sinda" lang="sd" hreflang="sd" data-title="ايراضي" data-language-autonym="سنڌي" data-language-local-name="sinda" 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 — serbo-Kroata" lang="sh" hreflang="sh" data-title="Površina" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbo-Kroata" 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) — slovaka" lang="sk" hreflang="sk" data-title="Plocha (útvar)" data-language-autonym="Slovenčina" data-language-local-name="slovaka" 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 — slovena" lang="sl" hreflang="sl" data-title="Površina" data-language-autonym="Slovenščina" data-language-local-name="slovena" 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 — ŝona" lang="sn" hreflang="sn" data-title="Nharaunda" data-language-autonym="ChiShona" data-language-local-name="ŝona" 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 — somala" lang="so" hreflang="so" data-title="Bed" data-language-autonym="Soomaaliga" data-language-local-name="somala" 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 — albana" lang="sq" hreflang="sq" data-title="Sipërfaqja" data-language-autonym="Shqip" data-language-local-name="albana" 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 — serba" lang="sr" hreflang="sr" data-title="Површина" data-language-autonym="Српски / srpski" data-language-local-name="serba" 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 — sunda" lang="su" hreflang="su" data-title="Aréa" data-language-autonym="Sunda" data-language-local-name="sunda" 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 — sveda" lang="sv" hreflang="sv" data-title="Area" data-language-autonym="Svenska" data-language-local-name="sveda" 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 — svahila" lang="sw" hreflang="sw" data-title="Eneo" data-language-autonym="Kiswahili" data-language-local-name="svahila" 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 — silezi-pola" lang="szl" hreflang="szl" data-title="Plac rozlygowańo" data-language-autonym="Ślůnski" data-language-local-name="silezi-pola" 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 — tamila" lang="ta" hreflang="ta" data-title="பரப்பளவு" data-language-autonym="தமிழ்" data-language-local-name="tamila" 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 — telugua" lang="te" hreflang="te" data-title="విస్తీర్ణం" data-language-autonym="తెలుగు" data-language-local-name="telugua" 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 — taĝika" lang="tg" hreflang="tg" data-title="Масоҳат" data-language-autonym="Тоҷикӣ" data-language-local-name="taĝika" 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 — taja" lang="th" hreflang="th" data-title="พื้นที่" data-language-autonym="ไทย" data-language-local-name="taja" 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 — tigraja" lang="ti" hreflang="ti" data-title="ጽፍሓት መሬት" data-language-autonym="ትግርኛ" data-language-local-name="tigraja" 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 — tagaloga" lang="tl" hreflang="tl" data-title="Sukat" data-language-autonym="Tagalog" data-language-local-name="tagaloga" 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 — turka" lang="tr" hreflang="tr" data-title="Alan" data-language-autonym="Türkçe" data-language-local-name="turka" 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 — tatara" lang="tt" hreflang="tt" data-title="Mäydan" data-language-autonym="Татарча / tatarça" data-language-local-name="tatara" 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 — ukraina" lang="uk" hreflang="uk" data-title="Площа" data-language-autonym="Українська" data-language-local-name="ukraina" 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 — urduo" lang="ur" hreflang="ur" data-title="رقبہ" data-language-autonym="اردو" data-language-local-name="urduo" 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 — uzbeka" lang="uz" hreflang="uz" data-title="Yuza" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbeka" 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 — vjetnama" lang="vi" hreflang="vi" data-title="Diện tích" data-language-autonym="Tiếng Việt" data-language-local-name="vjetnama" 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 — valona" lang="wa" hreflang="wa" data-title="Sitindêye" data-language-autonym="Walon" data-language-local-name="valona" 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 — varaja" lang="war" hreflang="war" data-title="Kahaluag" data-language-autonym="Winaray" data-language-local-name="varaja" 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 — volofa" lang="wo" hreflang="wo" data-title="Yaatuwaay" data-language-autonym="Wolof" data-language-local-name="volofa" 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 — vua" lang="wuu" hreflang="wuu" data-title="面积" data-language-autonym="吴语" data-language-local-name="vua" 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 — jida" lang="yi" hreflang="yi" data-title="שטח" data-language-autonym="ייִדיש" data-language-local-name="jida" 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 — joruba" lang="yo" hreflang="yo" data-title="Ààlà" data-language-autonym="Yorùbá" data-language-local-name="joruba" 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 — ĉina" lang="zh" hreflang="zh" data-title="面积" data-language-autonym="中文" data-language-local-name="ĉina" 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 — kantona" lang="yue" hreflang="yue" data-title="面積" data-language-autonym="粵語" data-language-local-name="kantona" 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="Redakti interlingvajn ligilojn" class="wbc-editpage">Redakti ligilojn</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="Nomspacoj"> <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/Areo" title="Vidi la artikolon [c]" accesskey="c"><span>Artikolo</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Diskuto:Areo&action=edit&redlink=1" rel="discussion" class="new" title="Diskuto pri la artikolo (paĝo ne ekzistas) [t]" accesskey="t"><span>Diskuto</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="Ŝanĝi lingvan varianton" > <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">Esperanto</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Vidoj"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Areo"><span>Legi</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Areo&veaction=edit" title="Redakti ĉi tiun paĝon [v]" accesskey="v"><span>Redakti</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Areo&action=edit" title="Redakti fontan kodon de tiu ĉi paĝo [e]" accesskey="e"><span>Redakti fonton</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Areo&action=history" title="Antaŭaj versioj de ĉi tiu paĝo. [h]" accesskey="h"><span>Vidi historion</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Paĝaj iloj"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Iloj" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-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">Iloj</span> </label> <div 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">Iloj</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">movigi al flanka panelo</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">kaŝi</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Pliaj opcioj" > <div class="vector-menu-heading"> Agoj </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/Areo"><span>Legi</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Areo&veaction=edit" title="Redakti ĉi tiun paĝon [v]" accesskey="v"><span>Redakti</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Areo&action=edit" title="Redakti fontan kodon de tiu ĉi paĝo [e]" accesskey="e"><span>Redakti fonton</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Areo&action=history"><span>Vidi historion</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Ĝenerale </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Speciala%C4%B5o:Kio_ligas_%C4%89i_tien%3F/Areo" title="Listo de ĉiuj vikiaj paĝoj kiuj ligas ĉi tien [j]" accesskey="j"><span>Ligiloj ĉi tien</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Speciala%C4%B5o:Rilataj_%C5%9Dan%C4%9Doj/Areo" rel="nofollow" title="Lastaj ŝanĝoj en paĝoj kiuj ligas al ĉi tiu paĝo [k]" accesskey="k"><span>Rilataj ŝanĝoj</span></a></li><li id="t-upload" class="mw-list-item"><a href="//commons.wikimedia.org/wiki/Special:UploadWizard?uselang=eo" title="Alŝuti dosierojn [u]" accesskey="u"><span>Alŝuti dosieron</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Areo&oldid=9043922" title="Porĉiama ligilo al ĉi versio de la paĝo"><span>Konstanta ligilo</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Areo&action=info" title="Pli da informo pri ĉi tiu paĝo"><span>Informoj pri la paĝo</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Speciala%C4%B5o:Citi&page=Areo&id=9043922&wpFormIdentifier=titleform" title="Informoj pri kiel citi ĉi tiun paĝon"><span>Citi ĉi tiun artikolon</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Speciala%C4%B5o:UrlShortener&url=https%3A%2F%2Feo.wikipedia.org%2Fwiki%2FAreo"><span>Akiri mallongigitan URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Speciala%C4%B5o:QrCode&url=https%3A%2F%2Feo.wikipedia.org%2Fwiki%2FAreo"><span>Elŝutu QR-kodon</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"> Presi/elporti </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=Speciala%C4%B5o:Libro&bookcmd=book_creator&referer=Areo"><span>Krei libron</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Speciala%C4%B5o:DownloadAsPdf&page=Areo&action=show-download-screen"><span>Elŝuti kiel PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Areo&printable=yes" title="Presebla versio de tiu ĉi paĝo [p]" accesskey="p"><span>Presebla versio</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"> En aliaj projektoj </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>Vikimedia Komunejo</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="Ligilo al konektita datuma ero [g]" accesskey="g"><span>Ero en Vikidatumoj</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="Paĝaj iloj"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Aspekto"> <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">Aspekto</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">movigi al flanka panelo</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">kaŝi</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">El Vikipedio, la libera enciklopedio</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="eo" dir="ltr"><p><b>Areo</b> (komparu: <a href="/wiki/Sanskrito" title="Sanskrito">sanskrite</a> <i>ur, urv, urw.ars</i> (tero); <a href="/wiki/Latina" class="mw-redirect" title="Latina">latine</a> <i>area</i> (<i>arvum</i>, kampo))<sup id="cite_ref-Azorín_1-0" class="reference"><a href="#cite_note-Azorín-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> estas la <a href="/wiki/Kvanto" title="Kvanto">kvanto</a> esprimanta la grandecon de regiono sur <a href="/wiki/Ebeno_(matematiko)" title="Ebeno (matematiko)">ebeno</a> aŭ, pli ĝenerale, <a href="/wiki/Mezuro" title="Mezuro">mezuron</a> de (ne nepre ebena) du<a href="/wiki/Dimensio" title="Dimensio">dimensia</a> <a href="/wiki/Surfaco" title="Surfaco">surfaco</a><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>. </p><p>Ekzemple, la areo de <a href="/wiki/Ortangulo" title="Ortangulo">ortangulo</a> estas kalkulata per la formulo <i>a</i><a href="/wiki/Multipliko" title="Multipliko">×</a><i>b</i>, kie <i>a</i> kaj <i>b</i> estas la <a href="/wiki/Longo" title="Longo">longo</a> kaj la <a href="/wiki/Lar%C4%9Do" title="Larĝo">larĝo</a> de la ortangulo. </p><p>La <a href="/wiki/Sistemo_Internacia_de_Unuoj" class="mw-redirect" title="Sistemo Internacia de Unuoj">SI-unuo</a> de areo estas <a href="/wiki/Kvadrata_metro" title="Kvadrata metro">kvadrata metro</a> (m<sup>2</sup>). Aliaj unuoj estas kvadrata <a href="/wiki/Kilometro" title="Kilometro">kilometro</a> ktp. kaj <a href="/wiki/Hektaro" title="Hektaro">hektaro</a> (100 m × 100 m = 10 000 m<sup>2</sup>). </p><p>La vorton <i>areo</i> oni uzas ankaŭ en alia senco: tiel oni nomas parton de la <a href="/wiki/Tera_surfaco" class="mw-redirect" title="Tera surfaco">tera surfaco</a> kun difinitaj <a href="/wiki/Limo" title="Limo">limoj</a> aŭ difinita uzo. Kutime estas klare, ĉu temas pri la areo mem aŭ pri la mezuro de ĝia grando, tamen oni konsciu, ke temas pri la uzado de la sama vorto por malsamaj nocioj. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Difinoj">Difinoj</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Areo&veaction=edit&section=1" title="Redakti sekcion: Difinoj" class="mw-editsection-visualeditor"><span>redakti</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Areo&action=edit&section=1" title="Redakti la fontkodo de la sekcio: Difinoj"><span>redakti fonton</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Laŭ <a href="/wiki/Francisko_Azor%C3%ADn" class="mw-redirect" title="Francisko Azorín">Francisko Azorín</a> <b>areo</b> estas <i>Tersurfaco. Spaco inter difinitaj limoj.</i><sup id="cite_ref-Azorín_1-1" class="reference"><a href="#cite_note-Azorín-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>Alproksimiĝo al difino de tio kio estas komprenata per "areo" estas kreita tra <a href="/wiki/Aksiomo" title="Aksiomo">aksiomoj</a>. "Areo" povas esti difinita kiel funkcio el kolekto M de speciala tipo de ebenaj figuroj (terminigite kiel mezureblaj surfacoj) al la serio de <a href="/wiki/Reelaj_nombroj" class="mw-redirect" title="Reelaj nombroj">reelaj nombroj</a>, kio plenumas la jenajn proprecojn: </p> <ul><li>Por ĉiu <i>S</i> en <i>M</i>, <i>a</i>(<i>S</i>) ≥ 0.</li> <li>Se <i>S</i> kaj <i>T</i> estas en <i>M</i> tiam estas ankaŭ <i>S</i> ∪ <i>T</i> kaj <i>S</i> ∩ <i>T</i>, kaj ankaŭ <i>a</i>(<i>S</i>∪<i>T</i>) = <i>a</i>(<i>S</i>) + <i>a</i>(<i>T</i>) − <i>a</i>(<i>S</i>∩<i>T</i>).</li> <li>Se <i>S</i> kaj <i>T</i> estas en <i>M</i> kun <i>S</i> ⊆ <i>T</i> tiam <i>T</i> − <i>S</i> estas en <i>M</i> kaj <i>a</i>(<i>T</i>−<i>S</i>) = <i>a</i>(<i>T</i>) − <i>a</i>(<i>S</i>).</li> <li>Se serio <i>S</i> estas en <i>M</i> kaj <i>S</i> estas kongrua kun <i>T</i> tiam <i>T</i> estas ankaŭ en <i>M</i> kaj <i>a</i>(<i>S</i>) = <i>a</i>(<i>T</i>).</li> <li>Ĉiu ortangulo <i>R</i> estas en <i>M</i>. Se la ortangulo havas longon <i>h</i> kaj larĝon <i>k</i> tiam <i>a</i>(<i>R</i>) = <i>hk</i>.</li> <li>Lasu <i>Q</i> esti serio ene de inter du ŝtupregionoj <i>S</i> kaj <i>T</i>. Ŝtupregiono estas formata el finita unio de apudaj ortanguloj restantaj sur komuna bazo, t.e. <i>S</i> ⊆ <i>Q</i> ⊆ <i>T</i>. Se estas unika nombro <i>c</i> tiel ke <i>a</i>(<i>S</i>) ≤ c ≤ <i>a</i>(<i>T</i>) por ĉiuj tiaj ŝtupregionoj <i>S</i> kaj <i>T</i>, tiam <i>a</i>(<i>Q</i>) = <i>c</i>.</li></ul> <p>Oni povas pruvi, ke tia areofunkcio fakte ekzistas.<sup id="cite_ref-Moise_3-0" class="reference"><a href="#cite_note-Moise-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Historio">Historio</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Areo&veaction=edit&section=2" title="Redakti sekcion: Historio" class="mw-editsection-visualeditor"><span>redakti</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Areo&action=edit&section=2" title="Redakti la fontkodo de la sekcio: Historio"><span>redakti fonton</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La ideo ke la areo estas la mezuro kiu havigas la grandon de la regiono enmetita en <a href="/wiki/Geometria_figuro" title="Geometria figuro">geometriaj figuroj</a> devenas de la <a href="/wiki/Antikveco" class="mw-redirect" title="Antikveco">Antikveco</a>. En la <a href="/wiki/Antikva_Egipto" class="mw-redirect" title="Antikva Egipto">antikva Egipto</a>, post la ĉiujara kreskiĝo fare de la rivero <a href="/wiki/Nilo" title="Nilo">Nilo</a> kiu inundis la kampojn, aperis la neceso kalkuli la areon de ĉiu agrikultura terpeco por restaŭri ties limojn; por solvi tion, la egiptoj inventis la <a href="/wiki/Geometrio" title="Geometrio">geometrion</a>, laŭ <a href="/wiki/Herodoto" title="Herodoto">Herodoto</a>.<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> </p><p>La maniero kalkuli la areon de <a href="/wiki/Plurlatero" title="Plurlatero">plurlatero</a> kiel la adicio de la areoj de trianguloj, estas metodo kiu estis proponita por la unua fojo fare de la greka fakulo <a href="/wiki/Antifono_(persono)" class="mw-redirect" title="Antifono (persono)">Antifono</a> ĉirkaŭ la jaro 430 a.n.e. Kalkuli la areon de kurba figuro generas plian malfacilecon. La elĉerpa metodo konsistas en la enmeto de plurlateroj en la geometria figuro, pligrandigi la nombron de flankoj de tiuj plurlateroj kaj kalkuli la celitan areon. Per tiu sistemo konata kiel <i>elĉerpa metodo</i> de <a href="/wiki/E%C5%ADdokso_el_Knido" title="Eŭdokso el Knido">Eŭdokso</a>, oni sukcesis atingi alproksimigon por kalkuli la areon de <a href="/wiki/Disko_(matematiko)" title="Disko (matematiko)">disko</a>. Tiu sistemo estis uzata poste fare de <a href="/wiki/Arkimedo" title="Arkimedo">Arkimedo</a> por solvi aliajn similajn problemojn,<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> same kiel la proksimuman kalkulon de la <a href="/wiki/Pi_(nombro)" title="Pi (nombro)">nombro π</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Area_de_ebenaj_figuroj">Area de ebenaj figuroj</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Areo&veaction=edit&section=3" title="Redakti sekcion: Area de ebenaj figuroj" class="mw-editsection-visualeditor"><span>redakti</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Areo&action=edit&section=3" title="Redakti la fontkodo de la sekcio: Area de ebenaj figuroj"><span>redakti fonton</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r8860200">.mw-parser-output .cxefartikolo{background-color:#f9f9f9;border:1px solid #aaa;padding:0.5em;font-style:italic}@media screen{html.skin-theme-clientpref-night .mw-parser-output .cxefartikolo{background-color:#202122;color:white;border:1px solid #333333}html.skin-theme-clientpref-light .mw-parser-output .cxefartikolo{background-color:#F9F9F9;color:black;border:1px solid #AAAAAA}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cxefartikolo{background-color:#202122;color:white;border:1px solid #333333}}</style> <div class="cxefartikolo" style="margin-bottom: 0.5em; border: 1px solid #ccc; padding: 2px; text-align: left; font-size: 95%;"><span typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/48/Loupe.svg/12px-Loupe.svg.png" decoding="async" width="12" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/48/Loupe.svg/18px-Loupe.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/48/Loupe.svg/24px-Loupe.svg.png 2x" data-file-width="58" data-file-height="57" /></span></span> Pli detalaj informoj troveblas en artikolo <a href="/wiki/Geometria_figuro" title="Geometria figuro">Geometria figuro</a>.</div> <div class="mw-heading mw-heading3"><h3 id="Areo_de_triangulo">Areo de triangulo</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Areo&veaction=edit&section=4" title="Redakti sekcion: Areo de triangulo" class="mw-editsection-visualeditor"><span>redakti</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Areo&action=edit&section=4" title="Redakti la fontkodo de la sekcio: Areo de triangulo"><span>redakti fonton</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Dosiero:Triangle_GeometryArea.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Triangle_GeometryArea.svg/300px-Triangle_GeometryArea.svg.png" decoding="async" width="300" height="75" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Triangle_GeometryArea.svg/450px-Triangle_GeometryArea.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Triangle_GeometryArea.svg/600px-Triangle_GeometryArea.svg.png 2x" data-file-width="473" data-file-height="119" /></a><figcaption>Kalkulo de la areo de triangulo <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 A={\tfrac {b\cdot h}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mrow> <mi>b</mi> <mo>⋅</mo> <mi>h</mi> </mrow> <mn>2</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A={\tfrac {b\cdot h}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d4d00ca1155c1418f0f6dcef9bdc0c9e4bb6236" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:7.787ex; height:3.676ex;" alt="{\displaystyle A={\tfrac {b\cdot h}{2}}}" /></span></figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/Dosiero:Area.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Area.svg/250px-Area.svg.png" decoding="async" width="214" height="214" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Area.svg/330px-Area.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Area.svg/500px-Area.svg.png 2x" data-file-width="800" data-file-height="800" /></a><figcaption>Areoj en <a href="/wiki/Ebeno_(matematiko)" title="Ebeno (matematiko)">kvadratita papero</a>.</figcaption></figure> <ul><li>La areo de <a href="/wiki/Triangulo" title="Triangulo">triangulo</a> estas egala al la duon-<a href="/wiki/Produto" title="Produto">produto</a> inter la longo de unu bazo kaj la alto relativa al tiu:<sup id="cite_ref-ref_duplicada_1_6-0" class="reference"><a href="#cite_note-ref_duplicada_1-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup></li></ul> <p><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 A={\frac {b\cdot h}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>b</mi> <mo>⋅</mo> <mi>h</mi> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A={\frac {b\cdot h}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ddcca4fc2882400f01bbf33b2dfa758d8942ba26" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:9.693ex; height:5.343ex;" alt="{\displaystyle A={\frac {b\cdot h}{2}}}" /></span> </p> <dl><dd>kie <i>b</i> estas la bazo de la triangulo kaj <i>h</i> estas la alto koresponda al tiu bazo (oni povas konsideri ajnan lateron kiel bazo).</dd></dl> <ul><li>Se la <a href="/wiki/Orta_triangulo" title="Orta triangulo">triangulo estas orta</a>, la alto koincidas kun unu el la <a href="/wiki/Kateto" title="Kateto">katetoj</a>, pro kio la areo estas egala al la duonproduto de la katetoj:</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 A={\frac {a\cdot b}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>a</mi> <mo>⋅</mo> <mi>b</mi> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A={\frac {a\cdot b}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3c48fa15935cd42e88f9d692579f8b94b7d2a4a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:9.584ex; height:5.343ex;" alt="{\displaystyle A={\frac {a\cdot b}{2}}}" /></span></dd> <dd>kie <i>a</i> kaj <i>b</i> estas la katetoj.</dd></dl> <ul><li>Se oni konas la longon de ties lateroj, oni povas apliki la <a href="/wiki/Formulo_de_Heron" class="mw-redirect" title="Formulo de Heron">formulon de Heron</a>.</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 A={\sqrt {s(s-a)(s-b)(s-c)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>s</mi> <mo stretchy="false">(</mo> <mi>s</mi> <mo>−</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>s</mi> <mo>−</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>s</mi> <mo>−</mo> <mi>c</mi> <mo stretchy="false">)</mo> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A={\sqrt {s(s-a)(s-b)(s-c)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f2040da62a4f48c9f502e3f38e44133524401c00" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:28.71ex; height:4.843ex;" alt="{\displaystyle A={\sqrt {s(s-a)(s-b)(s-c)}}}" /></span></dd></dl> <dl><dd>kie <i>a</i>, <i>b</i>, <i>c</i> estas la valoroj de la longoj de ties lateroj, <i>s</i> = ½ (<i>a</i> + <i>b</i> + <i>c</i>) estas la <b>duonperimetro</b> de la triangulo.</dd></dl> <ul><li>Se la <a href="/wiki/Egallatera_triangulo" title="Egallatera triangulo">triangulo estas egallatera</a>, la areo estas egala al unu kvarono de la kvadrato de unu latero por la <a href="/wiki/Kvadrata_radiko" title="Kvadrata radiko">kvadrata radiko</a> de 3:</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 A={\frac {{\sqrt {3}}\cdot a^{2}}{4}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> <mo>⋅</mo> <msup> <mi>a</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 A={\frac {{\sqrt {3}}\cdot a^{2}}{4}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/458b1e2fa62308ee9807d41841aa78adee9cd5d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:12.739ex; height:5.843ex;" alt="{\displaystyle A={\frac {{\sqrt {3}}\cdot a^{2}}{4}}}" /></span></dd></dl> <dl><dd>kie <i>a</i> estas unu latero de la triangulo.</dd></dl> <div class="mw-heading mw-heading3"><h3 id="Area_de_kvarlatero">Area de kvarlatero</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Areo&veaction=edit&section=5" title="Redakti sekcion: Area de kvarlatero" class="mw-editsection-visualeditor"><span>redakti</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Areo&action=edit&section=5" title="Redakti la fontkodo de la sekcio: Area de kvarlatero"><span>redakti fonton</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Dosiero:Tetragon_measures.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Tetragon_measures.svg/250px-Tetragon_measures.svg.png" decoding="async" width="200" height="222" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Tetragon_measures.svg/300px-Tetragon_measures.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Tetragon_measures.svg/400px-Tetragon_measures.svg.png 2x" data-file-width="324" data-file-height="360" /></a><figcaption>Trapezoido.</figcaption></figure> <ul><li>La areo de <a href="/wiki/Trapezoido" title="Trapezoido">trapezoido</a> aŭ de ajna <a href="/wiki/Kvarlatero" title="Kvarlatero">kvarlatero</a> estas egala al la duonproduto de ties diagonaloj por la <a href="/wiki/Sinuso_(matematiko)" title="Sinuso (matematiko)">sinuso</a> de la angulo kiun ili formas.</li></ul> <p><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 A={\frac {{\overline {AC}}\cdot {\overline {BD}}\cdot \sin \theta }{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>A</mi> <mi>C</mi> </mrow> <mo accent="false">¯</mo> </mover> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>B</mi> <mi>D</mi> </mrow> <mo accent="false">¯</mo> </mover> </mrow> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mi>θ</mi> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A={\frac {{\overline {AC}}\cdot {\overline {BD}}\cdot \sin \theta }{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1c59036ac101d1701f211db5a927df080dad20b4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:20.865ex; height:6.176ex;" alt="{\displaystyle A={\frac {{\overline {AC}}\cdot {\overline {BD}}\cdot \sin \theta }{2}}}" /></span> </p> <dl><dd>La areo estas atingebla ankaŭ pere de <a href="/wiki/Triangulado" title="Triangulado">triangulado</a>:</dd></dl> <p><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 A={\frac {a\cdot d\cdot \sin \alpha +b\cdot c\cdot \sin \gamma }{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>a</mi> <mo>⋅</mo> <mi>d</mi> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> <mo>+</mo> <mi>b</mi> <mo>⋅</mo> <mi>c</mi> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mi>γ</mi> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A={\frac {a\cdot d\cdot \sin \alpha +b\cdot c\cdot \sin \gamma }{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d55d005fa088a2c136d7a328cad7a7459febd8f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:28.92ex; height:5.343ex;" alt="{\displaystyle A={\frac {a\cdot d\cdot \sin \alpha +b\cdot c\cdot \sin \gamma }{2}}}" /></span> </p> <dl><dd>Estante: <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 \alpha \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mspace width="thinmathspace"></mspace> </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/652e1fd9c3a2ca00e1a517783cdbb0e18e4181f8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.875ex; height:1.676ex;" alt="{\displaystyle \alpha \,}" /></span> la angulo inter la lateroj <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 a\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d73aa5354c24942dab5316be466465a9d171510" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.617ex; height:1.676ex;" alt="{\displaystyle a\,}" /></span> kaj <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\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f203b686a923982358b9274fb508753ac31b996" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.603ex; height:2.176ex;" alt="{\displaystyle d\,}" /></span>.</dd> <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 \gamma \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>γ</mi> <mspace width="thinmathspace"></mspace> </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/65da7961fee8269d576e5d06e838bf8695fc5179" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.649ex; height:2.176ex;" alt="{\displaystyle \gamma \,}" /></span> la angulo inter la lateroj <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> <mspace width="thinmathspace"></mspace> </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/4b1bcf19f4ec75b1d2cc0be001e58a314fb0a940" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.385ex; height:2.176ex;" alt="{\displaystyle b\,}" /></span> kaj <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 c\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8573e7d95140b0d4068258d8162e189563baee6b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.394ex; height:1.676ex;" alt="{\displaystyle c\,}" /></span>.</dd></dl></dd></dl> <ul><li>La <a href="/wiki/Ortangulo" title="Ortangulo">ortangulo</a> estas plurlatero kies anguloj estas ĉiuj de 90º, kaj la areao estas egala al la produto de du el ties sinsekvaj lateroj <i>a</i> kaj <i>b</i>:<sup id="cite_ref-ref_duplicada_1_6-1" class="reference"><a href="#cite_note-ref_duplicada_1-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup></li></ul> <p><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 A={a\cdot b\,}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> <mo>⋅</mo> <mi>b</mi> <mspace width="thinmathspace"></mspace> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A={a\cdot b\,}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/22b7e1b42cef100bbdd46db5ce2ec10494b1fd84" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.135ex; height:2.176ex;" alt="{\displaystyle A={a\cdot b\,}}" /></span> </p> <ul><li>La <a href="/wiki/Rombo" title="Rombo">rombo</a> estas plurlatero kies 4 lateroj estas egalaj, kaj ties areo estas la duonproduto de ties du diagonaloj:</li></ul> <p><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 A={\frac {{\overline {AC}}\cdot {\overline {BD}}}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>A</mi> <mi>C</mi> </mrow> <mo accent="false">¯</mo> </mover> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>B</mi> <mi>D</mi> </mrow> <mo accent="false">¯</mo> </mover> </mrow> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A={\frac {{\overline {AC}}\cdot {\overline {BD}}}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/90fd4ebd7e95fb08d8171086319938fcf52620f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:14.852ex; height:6.176ex;" alt="{\displaystyle A={\frac {{\overline {AC}}\cdot {\overline {BD}}}{2}}}" /></span> </p> <ul><li>La <a href="/wiki/Kvadrato_(geometrio)" title="Kvadrato (geometrio)">kvadrato</a> estas la regula plurlatero de kvar lateroj; ĝi estas samtempe ortangulo kaj rombo, pro kio ĝia areo povas estis kalkulata sammaniere kiel tiuj de la ortangulo kaj de la rombo. Partikulare, ĉar ties lateroj estas egalaj, oni uzas la formulon:<sup id="cite_ref-ref_duplicada_1_6-2" class="reference"><a href="#cite_note-ref_duplicada_1-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup></li></ul> <p><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 A=a\cdot a\,=a^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mi>a</mi> <mo>⋅</mo> <mi>a</mi> <mspace width="thinmathspace"></mspace> <mo>=</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A=a\cdot a\,=a^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d65b422f2543331be4404812d397fe48b4527c05" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:14.75ex; height:2.676ex;" alt="{\displaystyle A=a\cdot a\,=a^{2}}" /></span> </p> <ul><li>La <a href="/wiki/Romboido" title="Romboido">romboido</a> havas areon kalkuleblan el la produto de unu de ties lateroj por la respektiva <a href="/wiki/Alto" title="Alto">alto</a>:<sup id="cite_ref-ref_duplicada_1_6-3" class="reference"><a href="#cite_note-ref_duplicada_1-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup></li></ul> <p><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 A=b\cdot h\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mi>b</mi> <mo>⋅</mo> <mi>h</mi> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A=b\cdot h\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/55194182f084f83d761e6b25f6b479b6470f9540" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.244ex; height:2.176ex;" alt="{\displaystyle A=b\cdot h\,}" /></span> </p> <ul><li>La <a href="/wiki/Trapezo" title="Trapezo">trapezo</a>, kiu havas du malajn laterojn paralelajn inter si kaj aliajn du neparalelajn laterojn, havas areon havigitan per la duonproduto de ties paralelaj lateroj multobligita por la distanco inter ili (alto):<sup id="cite_ref-ref_duplicada_1_6-4" class="reference"><a href="#cite_note-ref_duplicada_1-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup></li></ul> <p><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 A={\frac {a+b}{2}}\cdot h}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>a</mi> <mo>+</mo> <mi>b</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>⋅</mo> <mi>h</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A={\frac {a+b}{2}}\cdot h}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/88acc4bc72f097ef27daf84e7773366abe9b27a1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:13.764ex; height:5.343ex;" alt="{\displaystyle A={\frac {a+b}{2}}\cdot h}" /></span> </p><p>La areo de trapezo povas esti kalkulita kiel longo de la meza linio multiplikita per la distanco laŭ <a href="/wiki/Perpendikularo" title="Perpendikularo">perpendikularo</a> inter la paralelaj lateroj. Ĉi tio donas kiel speciala okazo la konatan formulon por la areo de <a href="/wiki/Triangulo" title="Triangulo">triangulo</a>, per konsidero de triangulo kiel <a href="/wiki/Degenera" class="mw-redirect" title="Degenera">degenera</a> trapezo ĉe kiu unu el la paralelaj lateroj estas malpligrandigita en punkton. Tial, se <i>a</i> kaj <i>b</i> estas la du paralelaj lateroj kaj <i>h</i> estas la distanco (alto) inter la paralelaj lateroj, la area formulo estas: </p> <dl><dd><i>A= (a+b)h/2</i></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Areo_de_la_disko_kaj_de_la_elipso">Areo de la disko kaj de la elipso</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Areo&veaction=edit&section=6" title="Redakti sekcion: Areo de la disko kaj de la elipso" class="mw-editsection-visualeditor"><span>redakti</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Areo&action=edit&section=6" title="Redakti la fontkodo de la sekcio: Areo de la disko kaj de la elipso"><span>redakti fonton</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La areo de <a href="/wiki/Disko_(matematiko)" title="Disko (matematiko)">disko</a>, nome tiu limigita de <a href="/wiki/Cirklo" title="Cirklo">cirklo</a>, estas kalkulebla pere de la jena matematika esprimo:<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p><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 A=\pi r^{2}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mi>π</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A=\pi r^{2}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dda045ad34ecde7c8e5573e84fabc7bccc58690c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.664ex; height:2.676ex;" alt="{\displaystyle A=\pi r^{2}\,}" /></span> </p> <figure typeof="mw:File/Thumb"><a href="/wiki/Dosiero:Areabetweentwographs.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Areabetweentwographs.svg/250px-Areabetweentwographs.svg.png" decoding="async" width="200" height="180" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Areabetweentwographs.svg/330px-Areabetweentwographs.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Areabetweentwographs.svg/500px-Areabetweentwographs.svg.png 2x" data-file-width="1000" data-file-height="900" /></a><figcaption>La areo limigita inter la bildo de du kurboj estas kalkulebla pere de la diferenco inter la integraloj de ambaŭ funkcioj.</figcaption></figure> <p>La areo limigita de <a href="/wiki/Elipso" class="mw-disambig" title="Elipso">elipso</a> estas simila kaj akirebla kiel produto de la duono de la plej granda akso por la duono de la malplej granda akso multobligitaj por π:<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p><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 A={\ \pi ab}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext> </mtext> <mi>π</mi> <mi>a</mi> <mi>b</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A={\ \pi ab}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd9bfb184b8f4232e074dc5b18632f12825f4798" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.982ex; height:2.176ex;" alt="{\displaystyle A={\ \pi ab}}" /></span> </p> <div class="mw-heading mw-heading3"><h3 id="Areo_limigita_inter_du_funkcioj">Areo limigita inter du funkcioj</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Areo&veaction=edit&section=7" title="Redakti sekcion: Areo limigita inter du funkcioj" class="mw-editsection-visualeditor"><span>redakti</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Areo&action=edit&section=7" title="Redakti la fontkodo de la sekcio: Areo limigita inter du funkcioj"><span>redakti fonton</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Metodo por atingi la areon limigita inter du <a href="/wiki/Funkcio_(matematiko)" title="Funkcio (matematiko)">funkcioj</a>, estas uzante la <a href="/wiki/Integralo" title="Integralo">integralan kalkulon</a>: </p><p><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 {\text{Areo}}(a,b)=\int _{a}^{b}|f(x)-g(x)|dx}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Areo</mtext> </mrow> <mo stretchy="false">(</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>g</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>d</mi> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{Areo}}(a,b)=\int _{a}^{b}|f(x)-g(x)|dx}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f4280c514d611677e7508acf99d79424f44fb5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:32.16ex; height:6.343ex;" alt="{\displaystyle {\text{Areo}}(a,b)=\int _{a}^{b}|f(x)-g(x)|dx}" /></span> </p><p>La rezulto de tiu integralo estas la areo enhavita inter la kurboj: <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 f(x)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78b2b66021c2cac2b5654495678c63ff142952e5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.805ex; height:2.843ex;" alt="{\displaystyle f(x)\,}" /></span> kaj <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 g(x)[<f(x)]\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>g</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">[</mo> <mo><</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">]</mo> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g(x)[<f(x)]\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a064a1435425a7eb665051170c682abc37bb7545" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.807ex; height:2.843ex;" alt="{\displaystyle g(x)[<f(x)]\,}" /></span> en la intermezo <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 [a,b]\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">]</mo> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [a,b]\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/23cb97ebba2cd3175f9a77446963c1849fc353ee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.942ex; height:2.843ex;" alt="{\displaystyle [a,b]\,}" /></span>. </p> <dl><dt>Ekzemplo</dt></dl> <p>Se oni deziras trovi la areon limigitan inter la akso x kaj la funkcio <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 f(x)=4-x^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>4</mn> <mo>−</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)=4-x^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6ed91cb47056d94beaafd7d78226581b52f0cec7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.903ex; height:3.176ex;" alt="{\displaystyle f(x)=4-x^{2}}" /></span> en la intermezo <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 [-2;2]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mo>−</mo> <mn>2</mn> <mo>;</mo> <mn>2</mn> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [-2;2]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3f5c033716eedc6610ea3bf46797743174c8c0bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.461ex; height:2.843ex;" alt="{\displaystyle [-2;2]}" /></span>, oni uzas la antaŭe menciitan ekvacion, tiuokaze: <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 g(x)=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>g</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g(x)=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2c9bb64a9a8234edd8fb1c622dddfab478719776" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.516ex; height:2.843ex;" alt="{\displaystyle g(x)=0}" /></span> tiam pritaksante la integralon, oni akiras jenon: </p><p><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 A(-2,2)=}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo stretchy="false">(</mo> <mo>−</mo> <mn>2</mn> <mo>,</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A(-2,2)=}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7e026dc5e9acad0510f12b21fe2aa7b0547c70d1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.173ex; height:2.843ex;" alt="{\displaystyle A(-2,2)=}" /></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 \int _{-2}^{2}|4-x^{2}-0|dx=}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mn>4</mn> <mo>−</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>0</mn> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>d</mi> <mi>x</mi> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{-2}^{2}|4-x^{2}-0|dx=}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/224928ee17c4d01bf1bd3012d67bd819a49615aa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:20.695ex; height:6.343ex;" alt="{\displaystyle \int _{-2}^{2}|4-x^{2}-0|dx=}" /></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 2\int _{0}^{2}4-x^{2}dx=}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mn>4</mn> <mo>−</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>d</mi> <mi>x</mi> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2\int _{0}^{2}4-x^{2}dx=}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43842e19f09c47e5a68ed4c837bb6ce88a127204" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:16.841ex; height:6.176ex;" alt="{\displaystyle 2\int _{0}^{2}4-x^{2}dx=}" /></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 2\left[4x-{\cfrac {x^{3}}{3}}\right]_{0}^{2}=}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <msubsup> <mrow> <mo>[</mo> <mrow> <mn>4</mn> <mi>x</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow></mrow> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow></mrow> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mrow> <mo>]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2\left[4x-{\cfrac {x^{3}}{3}}\right]_{0}^{2}=}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/80678e08bca7d8924f0dac17f1a5e33d793cf8bf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:15.933ex; height:8.176ex;" alt="{\displaystyle 2\left[4x-{\cfrac {x^{3}}{3}}\right]_{0}^{2}=}" /></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 2\left[8-\left({\cfrac {2^{3}-0}{3}}\right)\right]=}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mrow> <mo>[</mo> <mrow> <mn>8</mn> <mo>−</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow></mrow> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>−</mo> <mn>0</mn> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow></mrow> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mstyle> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mo>]</mo> </mrow> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2\left[8-\left({\cfrac {2^{3}-0}{3}}\right)\right]=}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b50b3078d58ba103ca92e16830f3c03b21700056" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:21.453ex; height:7.509ex;" alt="{\displaystyle 2\left[8-\left({\cfrac {2^{3}-0}{3}}\right)\right]=}" /></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 {\cfrac {32}{3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow></mrow> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mn>32</mn> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow></mrow> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\cfrac {32}{3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/29f4ce8da0adb746d55cff7c6a7cbf343ae41c53" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:3.161ex; height:7.176ex;" alt="{\displaystyle {\cfrac {32}{3}}}" /></span> </p><p>Pro kio oni konkludas, ke la areo limigita estas <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 32/3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>32</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 32/3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e470648eee6e9611ce750ad08eb153a36737ef90" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.65ex; height:2.843ex;" alt="{\displaystyle 32/3}" /></span>. </p><p>Ankaŭ la <a href="/wiki/Volumeno#Mezurunuoj" title="Volumeno">volumeno</a> enfermita inter du funkcioj povas esti atingebla per la kalkulo de simila integralo. </p> <div class="mw-heading mw-heading3"><h3 id="Rilato_areo-perimetro">Rilato areo-perimetro</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Areo&veaction=edit&section=8" title="Redakti sekcion: Rilato areo-perimetro" class="mw-editsection-visualeditor"><span>redakti</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Areo&action=edit&section=8" title="Redakti la fontkodo de la sekcio: Rilato areo-perimetro"><span>redakti fonton</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Difinita simpla kurbo enfermita en la eŭklida ebeno, oni povas pruvi, ke ties longo aŭ <a href="/wiki/Perimetro" title="Perimetro">perimetro</a> de la areo enfermita kaj la propra areo enfermita kongruas kun la rilato: </p><p><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 {A}{L^{2}}}\leq {\frac {1}{4\pi }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>A</mi> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>≤</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>4</mn> <mi>π</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {A}{L^{2}}}\leq {\frac {1}{4\pi }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b8b17bff61d8ec1135d0e22a173268a79036ab3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:9.902ex; height:5.509ex;" alt="{\displaystyle {\frac {A}{L^{2}}}\leq {\frac {1}{4\pi }}}" /></span> </p><p>La egaleco estas atingebla nur por disko; la ceteraj figuroj kaj eblaj formoj plenumas plej striktan malegalecon. </p> <div class="mw-heading mw-heading2"><h2 id="Disvastiĝa_areo"><span id="Disvasti.C4.9Da_areo"></span>Disvastiĝa areo</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Areo&veaction=edit&section=9" title="Redakti sekcion: Disvastiĝa areo" class="mw-editsection-visualeditor"><span>redakti</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Areo&action=edit&section=9" title="Redakti la fontkodo de la sekcio: Disvastiĝa areo"><span>redakti fonton</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><i>Disvastiĝa areo</i> estas esprimo por difini tiun teran surfacon de bestospecioj, kiun ili konkeris, tie ili disvastiĝis. Por tiu koncepto oni uzas ankaŭ la <a href="/wiki/Termino" class="mw-disambig" title="Termino">terminon</a> <a href="/wiki/Arealo" title="Arealo">arealo</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Bildaro">Bildaro</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Areo&veaction=edit&section=10" title="Redakti sekcion: Bildaro" class="mw-editsection-visualeditor"><span>redakti</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Areo&action=edit&section=10" title="Redakti la fontkodo de la sekcio: Bildaro"><span>redakti fonton</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul class="gallery mw-gallery-traditional"> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/Dosiero:PlotoMatai.png" class="mw-file-description" title="Komparoj de kvadrata futo kaj kvadrata jardo kun kvadrata metro."><img alt="Komparoj de kvadrata futo kaj kvadrata jardo kun kvadrata metro." src="//upload.wikimedia.org/wikipedia/commons/thumb/0/08/PlotoMatai.png/120px-PlotoMatai.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/08/PlotoMatai.png/180px-PlotoMatai.png 1.5x, //upload.wikimedia.org/wikipedia/commons/0/08/PlotoMatai.png 2x" data-file-width="240" data-file-height="240" /></a></span></div> <div class="gallerytext">Komparoj de kvadrata <a href="/wiki/Futo" title="Futo">futo</a> kaj kvadrata <a href="/wiki/Jardo" class="mw-disambig" title="Jardo">jardo</a> kun kvadrata <a href="/wiki/Metro" title="Metro">metro</a>.</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/Dosiero:Rectangle_2.svg" class="mw-file-description" title="La areo de ortangulo estas la produto de la longo kaj la larĝo"><img alt="La areo de ortangulo estas la produto de la longo kaj la larĝo" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/39/Rectangle_2.svg/120px-Rectangle_2.svg.png" decoding="async" width="120" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/39/Rectangle_2.svg/180px-Rectangle_2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/39/Rectangle_2.svg/240px-Rectangle_2.svg.png 2x" data-file-width="400" data-file-height="300" /></a></span></div> <div class="gallerytext">La areo de ortangulo estas la produto de la longo kaj la larĝo</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/Dosiero:Geometrie_carre.png" class="mw-file-description" title="La areo de kvadrato estas la kvadrato de la laterolongo"><img alt="La areo de kvadrato estas la kvadrato de la laterolongo" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b3/Geometrie_carre.png/120px-Geometrie_carre.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b3/Geometrie_carre.png/250px-Geometrie_carre.png 1.5x" data-file-width="342" data-file-height="343" /></a></span></div> <div class="gallerytext">La areo de <a href="/wiki/Kvadrato_(geometrio)" title="Kvadrato (geometrio)">kvadrato</a> estas la <a href="/wiki/Kvadrato_(algebro)" title="Kvadrato (algebro)">kvadrato</a> de la <a href="/wiki/Latero" title="Latero">laterolongo</a></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/Dosiero:Triangle-hauteur.png" class="mw-file-description" title="La areo de triangulo estas la duono de la produto de la latero kaj la alto rilata al tiu latero"><img alt="La areo de triangulo estas la duono de la produto de la latero kaj la alto rilata al tiu latero" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Triangle-hauteur.png/120px-Triangle-hauteur.png" decoding="async" width="120" height="52" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Triangle-hauteur.png/180px-Triangle-hauteur.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Triangle-hauteur.png/240px-Triangle-hauteur.png 2x" data-file-width="499" data-file-height="216" /></a></span></div> <div class="gallerytext">La areo de <a href="/wiki/Triangulo" title="Triangulo">triangulo</a> estas la duono de la produto de la latero kaj la <a href="/wiki/Alto" title="Alto">alto</a> rilata al tiu latero</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/Dosiero:An_ellipse_with_auxiliary_circle.svg" class="mw-file-description" title="La aero de elipso = '"`UNIQ--postMath-00000024-QINU`"'; la aero de la cirklo = '"`UNIQ--postMath-00000025-QINU`"'"><img alt="La aero de elipso = '"`UNIQ--postMath-00000024-QINU`"'; la aero de la cirklo = '"`UNIQ--postMath-00000025-QINU`"'" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/95/An_ellipse_with_auxiliary_circle.svg/120px-An_ellipse_with_auxiliary_circle.svg.png" decoding="async" width="120" height="111" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/95/An_ellipse_with_auxiliary_circle.svg/250px-An_ellipse_with_auxiliary_circle.svg.png 1.5x" data-file-width="327" data-file-height="302" /></a></span></div> <div class="gallerytext">La aero de <a href="/wiki/Elipso" class="mw-disambig" title="Elipso">elipso</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 \pi ab}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> <mi>a</mi> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi ab}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e49e097530aa054f7782fc7de33b0a60418ff964" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.559ex; height:2.176ex;" alt="{\displaystyle \pi ab}" /></span>; la aero de la <a href="/wiki/%C4%88irka%C5%ADskribita_cirklo" title="Ĉirkaŭskribita cirklo">cirklo</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 \pi a^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi a^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/36c8012cda8f5bcfe65a014d760eb7b676ad3055" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.616ex; height:2.676ex;" alt="{\displaystyle \pi a^{2}}" /></span></div> </li> </ul> <div class="mw-heading mw-heading2"><h2 id="Referencoj">Referencoj</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Areo&veaction=edit&section=11" title="Redakti sekcion: Referencoj" class="mw-editsection-visualeditor"><span>redakti</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Areo&action=edit&section=11" title="Redakti la fontkodo de la sekcio: Referencoj"><span>redakti fonton</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist references-small" style="padding-right: 6px;"> <ol class="references"> <li id="cite_note-Azorín-1">↑ <a href="#cite_ref-Azorín_1-0"><sup>1,0</sup></a> <a href="#cite_ref-Azorín_1-1"><sup>1,1</sup></a> <span class="reference-text"><a href="/wiki/Francisko_Azor%C3%ADn" class="mw-redirect" title="Francisko Azorín">Francisko Azorín</a>, arkitekto, <a href="/wiki/Universala_Terminologio_de_la_Arkitekturo" title="Universala Terminologio de la Arkitekturo">Universala Terminologio de la Arkitekturo</a> (arkeologio, arto, konstruo kaj metio), Presejo Chulilla y Ángel, Madrido, 1932, paĝo 18.</span> </li> <li id="cite_note-2"><a href="#cite_ref-2">↑</a> <span class="reference-text">Vd en <a href="/wiki/PIV" class="mw-redirect" title="PIV">PIV</a> kaj <a href="/wiki/ReVo" class="mw-redirect" title="ReVo">ReVo</a> "mezuro de surfaco" <a rel="nofollow" class="external autonumber" href="http://www.vortaro.net#areo">[1]</a></span> </li> <li id="cite_note-Moise-3"><a href="#cite_ref-Moise_3-0">↑</a> <span class="reference-text"><cite class="libro" style="font-style:normal;" id="referenco-Moise-1963">Moise, Edwin.  (1963) <i><a rel="nofollow" class="external text" href="https://archive.org/details/elementarygeomet0000mois">Elementary Geometry from an Advanced Standpoint</a></i>. Addison-Wesley Pub. Co..</cite> </span> </li> <li id="cite_note-4"><a href="#cite_ref-4">↑</a> <span class="reference-text">Herodoto <i>Historioj</i>, Libro II.</span> </li> <li id="cite_note-5"><a href="#cite_ref-5">↑</a> <span class="reference-text"><i>El problema del área</i>. fca.unl.edu.ar</span> </li> <li id="cite_note-ref_duplicada_1-6">↑ <a href="#cite_ref-ref_duplicada_1_6-0"><sup>6,0</sup></a> <a href="#cite_ref-ref_duplicada_1_6-1"><sup>6,1</sup></a> <a href="#cite_ref-ref_duplicada_1_6-2"><sup>6,2</sup></a> <a href="#cite_ref-ref_duplicada_1_6-3"><sup>6,3</sup></a> <a href="#cite_ref-ref_duplicada_1_6-4"><sup>6,4</sup></a> <span class="reference-text">Spiegel kaj Abellanas, 1992, p. 9</span> </li> <li id="cite_note-7"><a href="#cite_ref-7">↑</a> <span class="reference-text">Spiegel kaj Abellanas, 1992, p. 10</span> </li> <li id="cite_note-8"><a href="#cite_ref-8">↑</a> <span class="reference-text">Spiegel kaj Abellanas, 1992, p. 11.</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Literaturo">Literaturo</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Areo&veaction=edit&section=12" title="Redakti sekcion: Literaturo" class="mw-editsection-visualeditor"><span>redakti</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Areo&action=edit&section=12" title="Redakti la fontkodo de la sekcio: Literaturo"><span>redakti fonton</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Spiegel, Murray R.; Abellanas, Lorenzo (1992). McGraw-Hill, eld. <i>Fórmulas y tablas de matemática aplicada</i>. Aravaca (Madrid). <a href="/wiki/Speciala%C4%B5o:Citoj_el_libroj/8476151977" class="internal mw-magiclink-isbn">ISBN 84-7615-197-7</a>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Eksteraj_ligiloj">Eksteraj ligiloj</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Areo&veaction=edit&section=13" title="Redakti sekcion: Eksteraj ligiloj" class="mw-editsection-visualeditor"><span>redakti</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Areo&action=edit&section=13" title="Redakti la fontkodo de la sekcio: Eksteraj ligiloj"><span>redakti fonton</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="noprint" id="aliaj_projektoj" style="float: right; clear: right; width: 250px; border: 1px solid #aaa; padding: 4px; font-size: 90%; background: #f9f9f9;"> <ul class="noarchive"><li class="commons"><span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Area?uselang=eo">Kategorio Areo en la <span>Vikimedia Komunejo</span></a> (Multrimedaj datumoj)</span></li><li class="retavortaro"><a href="https://reta-vortaro.de/revo/art/are.html" class="extiw" title="revo:are">Areo en <span>ReVo</span></a> </li></ul> </div> <ul><li><a rel="nofollow" class="external free" href="http://www.shurey.com/Soft/JavaScript/DoRyouKou/square.html（Areo）">http://www.shurey.com/Soft/JavaScript/DoRyouKou/square.html（Areo）</a></li> <li><span class="plainlinks"><i>En tiu ĉi artikolo estas uzita traduko de teksto el la artikolo <a class="external text" href="https://es.wikipedia.org/w/index.php?title=%C3%81rea&oldid=126729273">Área</a> en la <a href="/w/index.php?title=%C5%9Cablono:Lingv/r&action=edit&redlink=1" class="new" title="Ŝablono:Lingv/r (paĝo ne ekzistas)">Ŝablono:Lingv/ra</a> Vikipedio. </i></span></li></ul> <div style="position:absolute; 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