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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">Início</div> </a> </li> <li id="toc-Definição" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Definição"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Definição</span> </div> </a> <button aria-controls="toc-Definição-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>Alternar a subsecção Definição</span> </button> <ul id="toc-Definição-sublist" class="vector-toc-list"> <li id="toc-Linha_poligonal" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Linha_poligonal"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Linha poligonal</span> </div> </a> <ul id="toc-Linha_poligonal-sublist" class="vector-toc-list"> <li id="toc-Classificação" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Classificação"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1.1</span> <span>Classificação</span> </div> </a> <ul id="toc-Classificação-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Polígono" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Polígono"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Polígono</span> </div> </a> <ul id="toc-Polígono-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Elementos" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Elementos"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Elementos</span> </div> </a> <button aria-controls="toc-Elementos-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>Alternar a subsecção Elementos</span> </button> <ul id="toc-Elementos-sublist" class="vector-toc-list"> <li id="toc-Exemplo" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Exemplo"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Exemplo</span> </div> </a> <ul id="toc-Exemplo-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Perímetro_e_Área" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Perímetro_e_Área"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Perímetro e Área</span> </div> </a> <ul id="toc-Perímetro_e_Área-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Classificação_2" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Classificação_2"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Classificação</span> </div> </a> <button aria-controls="toc-Classificação_2-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>Alternar a subsecção Classificação</span> </button> <ul id="toc-Classificação_2-sublist" class="vector-toc-list"> <li id="toc-Quanto_à_linha_poligonal" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Quanto_à_linha_poligonal"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Quanto à linha poligonal</span> </div> </a> <ul id="toc-Quanto_à_linha_poligonal-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Quanto_à_região_poligonal" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Quanto_à_região_poligonal"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Quanto à região poligonal</span> </div> </a> <ul id="toc-Quanto_à_região_poligonal-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Quanto_à_congruência" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Quanto_à_congruência"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Quanto à congruência</span> </div> </a> <ul id="toc-Quanto_à_congruência-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Quanto_ao_número_de_lados" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Quanto_ao_número_de_lados"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Quanto ao número de lados</span> </div> </a> <ul id="toc-Quanto_ao_número_de_lados-sublist" class="vector-toc-list"> <li id="toc-Nomenclatura_para_polígonos_com_muitos_lados" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Nomenclatura_para_polígonos_com_muitos_lados"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4.1</span> <span>Nomenclatura para polígonos com muitos lados</span> </div> </a> <ul id="toc-Nomenclatura_para_polígonos_com_muitos_lados-sublist" class="vector-toc-list"> <li id="toc-Exemplo_1" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Exemplo_1"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4.1.1</span> <span>Exemplo 1</span> </div> </a> <ul id="toc-Exemplo_1-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Exemplo_2" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Exemplo_2"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4.1.2</span> <span>Exemplo 2</span> </div> </a> <ul id="toc-Exemplo_2-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Propriedades" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Propriedades"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Propriedades</span> </div> </a> <button aria-controls="toc-Propriedades-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>Alternar a subsecção Propriedades</span> </button> <ul id="toc-Propriedades-sublist" class="vector-toc-list"> <li id="toc-Vértices_e_lados" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Vértices_e_lados"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Vértices e lados</span> </div> </a> <ul id="toc-Vértices_e_lados-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Diagonais" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Diagonais"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Diagonais</span> </div> </a> <ul id="toc-Diagonais-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ângulos" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ângulos"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Ângulos</span> </div> </a> <ul id="toc-Ângulos-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Mitologia" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Mitologia"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Mitologia</span> </div> </a> <ul id="toc-Mitologia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ver_também" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ver_também"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Ver também</span> </div> </a> <ul id="toc-Ver_também-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Referências" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Referências"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Referências</span> </div> </a> <ul id="toc-Referências-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ligações_externas" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ligações_externas"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Ligações externas</span> </div> </a> <ul id="toc-Ligações_externas-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="Conteúdo" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <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="Alternar o índice" > <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">Alternar o índice</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">Polígono</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="Ir para um artigo noutra língua. Disponível em 110 línguas" > <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-110" 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">110 línguas</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/Veelhoek" title="Veelhoek — africanês" lang="af" hreflang="af" data-title="Veelhoek" data-language-autonym="Afrikaans" data-language-local-name="africanês" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Poligono" title="Poligono — aragonês" lang="an" hreflang="an" data-title="Poligono" data-language-autonym="Aragonés" data-language-local-name="aragonês" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%B6%D9%84%D8%B9" title="مضلع — árabe" lang="ar" hreflang="ar" data-title="مضلع" data-language-autonym="العربية" data-language-local-name="árabe" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%AC%E0%A6%B9%E0%A7%81%E0%A6%AD%E0%A7%81%E0%A6%9C" title="বহুভুজ — assamês" lang="as" hreflang="as" data-title="বহুভুজ" data-language-autonym="অসমীয়া" data-language-local-name="assamês" 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/Pol%C3%ADgonu" title="Polígonu — asturiano" lang="ast" hreflang="ast" data-title="Polígonu" data-language-autonym="Asturianu" data-language-local-name="asturiano" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/%C3%87oxbucaql%C4%B1" title="Çoxbucaqlı — azerbaijano" lang="az" hreflang="az" data-title="Çoxbucaqlı" data-language-autonym="Azərbaycanca" data-language-local-name="azerbaijano" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%9A%D2%AF%D0%BF%D0%BC%D3%A9%D0%B9%D3%A9%D1%88" title="Күпмөйөш — bashkir" lang="ba" hreflang="ba" data-title="Күпмөйөш" data-language-autonym="Башҡортса" data-language-local-name="bashkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Poligono" title="Poligono — Central Bikol" lang="bcl" hreflang="bcl" data-title="Poligono" 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%9C%D0%BD%D0%BE%D0%B3%D0%B0%D0%B2%D1%83%D0%B3%D0%BE%D0%BB%D1%8C%D0%BD%D1%96%D0%BA" title="Многавугольнік — bielorrusso" lang="be" hreflang="be" data-title="Многавугольнік" data-language-autonym="Беларуская" data-language-local-name="bielorrusso" 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%A8%D0%BC%D0%B0%D1%82%D0%BA%D1%83%D1%82%D0%BD%D1%96%D0%BA" title="Шматкутнік — Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Шматкутнік" 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%9C%D0%BD%D0%BE%D0%B3%D0%BE%D1%8A%D0%B3%D1%8A%D0%BB%D0%BD%D0%B8%D0%BA" title="Многоъгълник — búlgaro" lang="bg" hreflang="bg" data-title="Многоъгълник" data-language-autonym="Български" data-language-local-name="búlgaro" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AC%E0%A6%B9%E0%A7%81%E0%A6%AD%E0%A7%81%E0%A6%9C" title="বহুভুজ — bengalês" lang="bn" hreflang="bn" data-title="বহুভুজ" data-language-autonym="বাংলা" data-language-local-name="bengalês" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Mnogougao" title="Mnogougao — bósnio" lang="bs" hreflang="bs" data-title="Mnogougao" data-language-autonym="Bosanski" data-language-local-name="bósnio" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Pol%C3%ADgon" title="Polígon — catalão" lang="ca" hreflang="ca" data-title="Polígon" data-language-autonym="Català" data-language-local-name="catalão" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%81%D8%B1%DB%95%DA%AF%DB%86%D8%B4%DB%95" title="فرەگۆشە — curdo central" lang="ckb" hreflang="ckb" data-title="فرەگۆشە" data-language-autonym="کوردی" data-language-local-name="curdo central" 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/Mnoho%C3%BAheln%C3%ADk" title="Mnohoúhelník — checo" lang="cs" hreflang="cs" data-title="Mnohoúhelník" data-language-autonym="Čeština" data-language-local-name="checo" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9D%D1%83%D0%BC%D0%B0%D0%B9%D0%BA%C4%95%D1%82%D0%B5%D1%81%D0%BB%C4%95%D1%85" title="Нумайкĕтеслĕх — chuvash" lang="cv" hreflang="cv" data-title="Нумайкĕтеслĕх" data-language-autonym="Чӑвашла" data-language-local-name="chuvash" 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/Polygon" title="Polygon — galês" lang="cy" hreflang="cy" data-title="Polygon" data-language-autonym="Cymraeg" data-language-local-name="galês" 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/Polygon" title="Polygon — dinamarquês" lang="da" hreflang="da" data-title="Polygon" data-language-autonym="Dansk" data-language-local-name="dinamarquês" 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/Polygon" title="Polygon — alemão" lang="de" hreflang="de" data-title="Polygon" data-language-autonym="Deutsch" data-language-local-name="alemão" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A0%CE%BF%CE%BB%CF%8D%CE%B3%CF%89%CE%BD%CE%BF" title="Πολύγωνο — grego" lang="el" hreflang="el" data-title="Πολύγωνο" data-language-autonym="Ελληνικά" data-language-local-name="grego" 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/Polygon" title="Polygon — inglês" lang="en" hreflang="en" data-title="Polygon" data-language-autonym="English" data-language-local-name="inglês" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Plurlatero" title="Plurlatero — esperanto" lang="eo" hreflang="eo" data-title="Plurlatero" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Pol%C3%ADgono" title="Polígono — espanhol" lang="es" hreflang="es" data-title="Polígono" data-language-autonym="Español" data-language-local-name="espanhol" 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/Hulknurk" title="Hulknurk — estónio" lang="et" hreflang="et" data-title="Hulknurk" data-language-autonym="Eesti" data-language-local-name="estónio" 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/Poligono" title="Poligono — basco" lang="eu" hreflang="eu" data-title="Poligono" data-language-autonym="Euskara" data-language-local-name="basco" 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/%DA%86%D9%86%D8%AF%D8%B6%D9%84%D8%B9%DB%8C" title="چندضلعی — persa" lang="fa" hreflang="fa" data-title="چندضلعی" 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/Monikulmio" title="Monikulmio — finlandês" lang="fi" hreflang="fi" data-title="Monikulmio" data-language-autonym="Suomi" data-language-local-name="finlandês" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Polygone" title="Polygone — francês" lang="fr" hreflang="fr" data-title="Polygone" data-language-autonym="Français" data-language-local-name="francês" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Polag%C3%A1n" title="Polagán — irlandês" lang="ga" hreflang="ga" data-title="Polagán" data-language-autonym="Gaeilge" data-language-local-name="irlandês" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Poligonn" title="Poligonn — Guianan Creole" lang="gcr" hreflang="gcr" data-title="Poligonn" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/Poileagan" title="Poileagan — gaélico escocês" lang="gd" hreflang="gd" data-title="Poileagan" data-language-autonym="Gàidhlig" data-language-local-name="gaélico escocês" 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/Pol%C3%ADgono" title="Polígono — galego" lang="gl" hreflang="gl" data-title="Polígono" data-language-autonym="Galego" data-language-local-name="galego" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%AC%E0%AA%B9%E0%AB%81%E0%AA%95%E0%AB%8B%E0%AA%A3" title="બહુકોણ — guzerate" lang="gu" hreflang="gu" data-title="બહુકોણ" data-language-autonym="ગુજરાતી" data-language-local-name="guzerate" 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/Yl-lhiatteean" title="Yl-lhiatteean — manx" lang="gv" hreflang="gv" data-title="Yl-lhiatteean" data-language-autonym="Gaelg" data-language-local-name="manx" 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/T%C3%B4-pi%C3%AAn-h%C3%ACn" title="Tô-piên-hìn — hacá" lang="hak" hreflang="hak" data-title="Tô-piên-hìn" data-language-autonym="客家語 / Hak-kâ-ngî" data-language-local-name="hacá" class="interlanguage-link-target"><span>客家語 / Hak-kâ-ngî</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A6%D7%95%D7%9C%D7%A2" title="מצולע — hebraico" lang="he" hreflang="he" data-title="מצולע" data-language-autonym="עברית" data-language-local-name="hebraico" 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%AC%E0%A4%B9%E0%A5%81%E0%A4%AD%E0%A5%81%E0%A4%9C" title="बहुभुज — hindi" lang="hi" hreflang="hi" data-title="बहुभुज" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Mnogokut" title="Mnogokut — croata" lang="hr" hreflang="hr" data-title="Mnogokut" data-language-autonym="Hrvatski" data-language-local-name="croata" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Polig%C3%B2n" title="Poligòn — haitiano" lang="ht" hreflang="ht" data-title="Poligòn" data-language-autonym="Kreyòl ayisyen" data-language-local-name="haitiano" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Soksz%C3%B6g" title="Sokszög — húngaro" lang="hu" hreflang="hu" data-title="Sokszög" data-language-autonym="Magyar" data-language-local-name="húngaro" 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/%D4%B2%D5%A1%D5%A6%D5%B4%D5%A1%D5%B6%D5%AF%D5%B5%D5%B8%D6%82%D5%B6" title="Բազմանկյուն — arménio" lang="hy" hreflang="hy" data-title="Բազմանկյուն" data-language-autonym="Հայերեն" data-language-local-name="arménio" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Poligon" title="Poligon — indonésio" lang="id" hreflang="id" data-title="Poligon" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonésio" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Poligono" title="Poligono — ido" lang="io" hreflang="io" data-title="Poligono" 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/Marghyrningur" title="Marghyrningur — islandês" lang="is" hreflang="is" data-title="Marghyrningur" data-language-autonym="Íslenska" data-language-local-name="islandês" 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/Poligono" title="Poligono — italiano" lang="it" hreflang="it" data-title="Poligono" data-language-autonym="Italiano" data-language-local-name="italiano" 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/%E5%A4%9A%E8%A7%92%E5%BD%A2" title="多角形 — japonês" lang="ja" hreflang="ja" data-title="多角形" data-language-autonym="日本語" data-language-local-name="japonês" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9B%E1%83%A0%E1%83%90%E1%83%95%E1%83%90%E1%83%9A%E1%83%99%E1%83%A3%E1%83%97%E1%83%AE%E1%83%94%E1%83%93%E1%83%98" title="მრავალკუთხედი — georgiano" lang="ka" hreflang="ka" data-title="მრავალკუთხედი" data-language-autonym="ქართული" data-language-local-name="georgiano" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kbd mw-list-item"><a href="https://kbd.wikipedia.org/wiki/%D0%9F%D0%BB%D3%80%D0%B0%D0%BD%D1%8D%D0%BF%D1%8D%D0%BA%D1%83%D1%8D%D0%B4" title="ПлӀанэпэкуэд — cabardiano" lang="kbd" hreflang="kbd" data-title="ПлӀанэпэкуэд" data-language-autonym="Адыгэбзэ" data-language-local-name="cabardiano" 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%9A%D3%A9%D0%BF%D0%B1%D2%B1%D1%80%D1%8B%D1%88" title="Көпбұрыш — cazaque" lang="kk" hreflang="kk" data-title="Көпбұрыш" data-language-autonym="Қазақша" data-language-local-name="cazaque" 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%96%E1%9E%A0%E1%9E%BB%E1%9E%80%E1%9F%84%E1%9E%8E" title="ពហុកោណ — khmer" lang="km" hreflang="km" data-title="ពហុកោណ" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="khmer" 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%8B%A4%EA%B0%81%ED%98%95" title="다각형 — coreano" lang="ko" hreflang="ko" data-title="다각형" data-language-autonym="한국어" data-language-local-name="coreano" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Pirgo%C5%9Fe" title="Pirgoşe — curdo" lang="ku" hreflang="ku" data-title="Pirgoşe" data-language-autonym="Kurdî" data-language-local-name="curdo" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%9A%D3%A9%D0%BF_%D0%B1%D1%83%D1%80%D1%87%D1%82%D1%83%D0%BA" title="Көп бурчтук — quirguiz" lang="ky" hreflang="ky" data-title="Көп бурчтук" data-language-autonym="Кыргызча" data-language-local-name="quirguiz" 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/Polygonum" title="Polygonum — latim" lang="la" hreflang="la" data-title="Polygonum" data-language-autonym="Latina" data-language-local-name="latim" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Poligon" title="Poligon — Lingua Franca Nova" lang="lfn" hreflang="lfn" data-title="Poligon" data-language-autonym="Lingua Franca Nova" data-language-local-name="Lingua Franca Nova" class="interlanguage-link-target"><span>Lingua Franca Nova</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Pol%C3%ACgon_(geometr%C3%ACa)" title="Polìgon (geometrìa) — lombardo" lang="lmo" hreflang="lmo" data-title="Polìgon (geometrìa)" data-language-autonym="Lombard" data-language-local-name="lombardo" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Daugiakampis" title="Daugiakampis — lituano" lang="lt" hreflang="lt" data-title="Daugiakampis" data-language-autonym="Lietuvių" data-language-local-name="lituano" 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/Daudzst%C5%ABris" title="Daudzstūris — letão" lang="lv" hreflang="lv" data-title="Daudzstūris" data-language-autonym="Latviešu" data-language-local-name="letão" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mdf mw-list-item"><a href="https://mdf.wikipedia.org/wiki/%D0%9B%D0%B0%D0%BC%D1%83%D0%B6%D0%B5%D0%BA%D1%81%D1%81%D1%8C" title="Ламужекссь — mocsa" lang="mdf" hreflang="mdf" data-title="Ламужекссь" data-language-autonym="Мокшень" data-language-local-name="mocsa" class="interlanguage-link-target"><span>Мокшень</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Marolafy_(je%C3%B4metria)" title="Marolafy (jeômetria) — malgaxe" lang="mg" hreflang="mg" data-title="Marolafy (jeômetria)" data-language-autonym="Malagasy" data-language-local-name="malgaxe" 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%A8%D1%83%D0%BA%D1%8B%D0%BB%D1%83%D0%BA" title="Шукылук — Eastern Mari" lang="mhr" hreflang="mhr" data-title="Шукылук" 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%9C%D0%BD%D0%BE%D0%B3%D1%83%D0%B0%D0%B3%D0%BE%D0%BB%D0%BD%D0%B8%D0%BA" title="Многуаголник — macedónio" lang="mk" hreflang="mk" data-title="Многуаголник" data-language-autonym="Македонски" data-language-local-name="macedónio" 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%AC%E0%B4%B9%E0%B5%81%E0%B4%AD%E0%B5%81%E0%B4%9C%E0%B4%82" title="ബഹുഭുജം — malaiala" lang="ml" hreflang="ml" data-title="ബഹുഭുജം" data-language-autonym="മലയാളം" data-language-local-name="malaiala" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Poligon" title="Poligon — malaio" lang="ms" hreflang="ms" data-title="Poligon" data-language-autonym="Bahasa Melayu" data-language-local-name="malaio" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%97%E1%80%9F%E1%80%AF%E1%80%82%E1%80%B6" title="ဗဟုဂံ — birmanês" lang="my" hreflang="my" data-title="ဗဟုဂံ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="birmanês" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Veeleck" title="Veeleck — baixo-alemão" lang="nds" hreflang="nds" data-title="Veeleck" data-language-autonym="Plattdüütsch" data-language-local-name="baixo-alemão" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%AC%E0%A4%B9%E0%A5%81%E0%A4%AD%E0%A5%81%E0%A4%9C" title="बहुभुज — nepalês" lang="ne" hreflang="ne" data-title="बहुभुज" data-language-autonym="नेपाली" data-language-local-name="nepalês" 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/Veelhoek" title="Veelhoek — neerlandês" lang="nl" hreflang="nl" data-title="Veelhoek" data-language-autonym="Nederlands" data-language-local-name="neerlandês" 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/Mangekant" title="Mangekant — norueguês nynorsk" lang="nn" hreflang="nn" data-title="Mangekant" data-language-autonym="Norsk nynorsk" data-language-local-name="norueguês nynorsk" 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/Polygon" title="Polygon — norueguês bokmål" lang="nb" hreflang="nb" data-title="Polygon" data-language-autonym="Norsk bokmål" data-language-local-name="norueguês bokmål" 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/Polig%C3%B2n" title="Poligòn — occitano" lang="oc" hreflang="oc" data-title="Poligòn" data-language-autonym="Occitan" data-language-local-name="occitano" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Rogbaayyee" title="Rogbaayyee — oromo" lang="om" hreflang="om" data-title="Rogbaayyee" data-language-autonym="Oromoo" data-language-local-name="oromo" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%AC%E0%A8%B9%E0%A9%81%E0%A8%AC%E0%A8%BE%E0%A8%B9%E0%A9%80%E0%A8%86" title="ਬਹੁਬਾਹੀਆ — panjabi" lang="pa" hreflang="pa" data-title="ਬਹੁਬਾਹੀਆ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="panjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Wielok%C4%85t" title="Wielokąt — polaco" lang="pl" hreflang="pl" data-title="Wielokąt" data-language-autonym="Polski" data-language-local-name="polaco" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%DA%85%D9%88_%D8%B6%D9%84%D8%B9%D9%8A" title="څو ضلعي — pastó" lang="ps" hreflang="ps" data-title="څو ضلعي" data-language-autonym="پښتو" data-language-local-name="pastó" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Ashkamanya_(pacha_tupuy)" title="Ashkamanya (pacha tupuy) — quíchua" lang="qu" hreflang="qu" data-title="Ashkamanya (pacha tupuy)" data-language-autonym="Runa Simi" data-language-local-name="quíchua" 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/Poligon" title="Poligon — romeno" lang="ro" hreflang="ro" data-title="Poligon" data-language-autonym="Română" data-language-local-name="romeno" 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%9C%D0%BD%D0%BE%D0%B3%D0%BE%D1%83%D0%B3%D0%BE%D0%BB%D1%8C%D0%BD%D0%B8%D0%BA" title="Многоугольник — russo" lang="ru" hreflang="ru" data-title="Многоугольник" data-language-autonym="Русский" data-language-local-name="russo" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Pul%C3%ACgunu" title="Pulìgunu — siciliano" lang="scn" hreflang="scn" data-title="Pulìgunu" data-language-autonym="Sicilianu" data-language-local-name="siciliano" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Poligon" title="Poligon — servo-croata" lang="sh" hreflang="sh" data-title="Poligon" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="servo-croata" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%B6%E0%B7%84%E0%B7%94%E0%B6%85%E0%B7%83%E0%B7%8A%E2%80%8D%E0%B6%BB" title="බහුඅස්‍ර — cingalês" lang="si" hreflang="si" data-title="බහුඅස්‍ර" data-language-autonym="සිංහල" data-language-local-name="cingalês" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Polygon" title="Polygon — Simple English" lang="en-simple" hreflang="en-simple" data-title="Polygon" 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/Mnohouholn%C3%ADk" title="Mnohouholník — eslovaco" lang="sk" hreflang="sk" data-title="Mnohouholník" data-language-autonym="Slovenčina" data-language-local-name="eslovaco" 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/Mnogokotnik" title="Mnogokotnik — esloveno" lang="sl" hreflang="sl" data-title="Mnogokotnik" data-language-autonym="Slovenščina" data-language-local-name="esloveno" 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/Gonyozhinji" title="Gonyozhinji — shona" lang="sn" hreflang="sn" data-title="Gonyozhinji" data-language-autonym="ChiShona" data-language-local-name="shona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Shum%C3%ABk%C3%ABnd%C3%ABshi" title="Shumëkëndëshi — albanês" lang="sq" hreflang="sq" data-title="Shumëkëndëshi" data-language-autonym="Shqip" data-language-local-name="albanês" 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%9C%D0%BD%D0%BE%D0%B3%D0%BE%D1%83%D0%B3%D0%B0%D0%BE" title="Многоугао — sérvio" lang="sr" hreflang="sr" data-title="Многоугао" data-language-autonym="Српски / srpski" data-language-local-name="sérvio" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Polygon" title="Polygon — sueco" lang="sv" hreflang="sv" data-title="Polygon" data-language-autonym="Svenska" data-language-local-name="sueco" 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/Pembenyingi" title="Pembenyingi — suaíli" lang="sw" hreflang="sw" data-title="Pembenyingi" data-language-autonym="Kiswahili" data-language-local-name="suaíli" 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/Wjeloek" title="Wjeloek — Silesian" lang="szl" hreflang="szl" data-title="Wjeloek" data-language-autonym="Ślůnski" data-language-local-name="Silesian" 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%B2%E0%AF%8D%E0%AE%95%E0%AF%8B%E0%AE%A3%E0%AE%AE%E0%AF%8D" title="பல்கோணம் — tâmil" lang="ta" hreflang="ta" data-title="பல்கோணம்" data-language-autonym="தமிழ்" data-language-local-name="tâmil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%91%D0%B8%D1%81%D1%91%D1%80%D0%BA%D1%83%D0%BD%D2%B7%D0%B0" title="Бисёркунҷа — tajique" lang="tg" hreflang="tg" data-title="Бисёркунҷа" data-language-autonym="Тоҷикӣ" data-language-local-name="tajique" 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%A3%E0%B8%B9%E0%B8%9B%E0%B8%AB%E0%B8%A5%E0%B8%B2%E0%B8%A2%E0%B9%80%E0%B8%AB%E0%B8%A5%E0%B8%B5%E0%B9%88%E0%B8%A2%E0%B8%A1" title="รูปหลายเหลี่ยม — tailandês" lang="th" hreflang="th" data-title="รูปหลายเหลี่ยม" data-language-autonym="ไทย" data-language-local-name="tailandês" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Poligon" title="Poligon — tagalo" lang="tl" hreflang="tl" data-title="Poligon" data-language-autonym="Tagalog" data-language-local-name="tagalo" 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/%C3%87okgen" title="Çokgen — turco" lang="tr" hreflang="tr" data-title="Çokgen" data-language-autonym="Türkçe" data-language-local-name="turco" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9C%D0%BD%D0%BE%D0%B3%D0%BE%D0%BA%D1%83%D1%82%D0%BD%D0%B8%D0%BA" title="Многокутник — ucraniano" lang="uk" hreflang="uk" data-title="Многокутник" data-language-autonym="Українська" data-language-local-name="ucraniano" 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/%DA%A9%D8%AB%DB%8C%D8%B1%D8%A7%D9%84%D8%A7%D8%B6%D9%84%D8%A7%D8%B9" title="کثیرالاضلاع — urdu" lang="ur" hreflang="ur" data-title="کثیرالاضلاع" data-language-autonym="اردو" data-language-local-name="urdu" 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/Ko%CA%BBpburchak" title="Koʻpburchak — usbeque" lang="uz" hreflang="uz" data-title="Koʻpburchak" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="usbeque" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/Po%C5%82igono" title="Połigono — Venetian" lang="vec" hreflang="vec" data-title="Połigono" data-language-autonym="Vèneto" data-language-local-name="Venetian" class="interlanguage-link-target"><span>Vèneto</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/%C4%90a_gi%C3%A1c" title="Đa giác — vietnamita" lang="vi" hreflang="vi" data-title="Đa giác" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamita" 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/Veelhoek" title="Veelhoek — West Flemish" lang="vls" hreflang="vls" data-title="Veelhoek" 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-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Puligunu" title="Puligunu — waray" lang="war" hreflang="war" data-title="Puligunu" data-language-autonym="Winaray" data-language-local-name="waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%A4%9A%E8%BE%B9%E5%BD%A2" title="多边形 — wu" lang="wuu" hreflang="wuu" data-title="多边形" data-language-autonym="吴语" data-language-local-name="wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A4%D7%99%D7%9C%D7%A2%D7%A7" title="פילעק — iídiche" lang="yi" hreflang="yi" data-title="פילעק" data-language-autonym="ייִדיש" data-language-local-name="iídiche" 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/An%C3%ADgunp%C3%BAp%E1%BB%8D%CC%80" title="Anígunpúpọ̀ — ioruba" lang="yo" hreflang="yo" data-title="Anígunpúpọ̀" data-language-autonym="Yorùbá" data-language-local-name="ioruba" class="interlanguage-link-target"><span>Yorùbá</span></a></li><li class="interlanguage-link interwiki-zgh mw-list-item"><a href="https://zgh.wikipedia.org/wiki/%E2%B4%B0%E2%B4%B3%E2%B5%9C%E2%B4%B7%E2%B5%89%E2%B5%99" title="ⴰⴳⵜⴷⵉⵙ — tamazight marroquino padrão" lang="zgh" hreflang="zgh" data-title="ⴰⴳⵜⴷⵉⵙ" data-language-autonym="ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ" data-language-local-name="tamazight marroquino padrão" class="interlanguage-link-target"><span>ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%A4%9A%E8%BE%B9%E5%BD%A2" title="多边形 — chinês" lang="zh" hreflang="zh" data-title="多边形" data-language-autonym="中文" data-language-local-name="chinês" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E5%A4%9A%E9%82%8A%E5%BD%A2" title="多邊形 — Literary Chinese" lang="lzh" hreflang="lzh" data-title="多邊形" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%A4%9A%E9%82%8A%E5%BD%A2" title="多邊形 — cantonês" lang="yue" hreflang="yue" data-title="多邊形" data-language-autonym="粵語" data-language-local-name="cantonês" 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/Q37555#sitelinks-wikipedia" title="Editar hiperligações interlínguas" class="wbc-editpage">Editar hiperligações</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="Espaços nominais"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs 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.tmbox.mbox-small{clear:right;float:right;margin:4px 0 4px 1em;width:238px}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .tmbox{background-color:#2e2505}html.skin-theme-clientpref-night .mw-parser-output .tmbox-speedy{background-color:#310402}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmbox{background-color:#2e2505}html.skin-theme-clientpref-os .mw-parser-output .tmbox-speedy{background-color:#310402}}body.skin--responsive .mw-parser-output table.tmbox img{max-width:none!important}</style><table class="box-Mais_notas plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div style="width:52px"><span typeof="mw:File"><a href="/wiki/Ficheiro:Question_book-new.svg" class="mw-file-description"><img alt="Esta página cita fontes, mas não cobrem todo o conteúdo" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">Este artigo <a href="/wiki/Wikip%C3%A9dia:Livro_de_estilo/Cite_as_fontes" title="Wikipédia:Livro de estilo/Cite as fontes">cita fontes</a>, mas que <b><a href="/wiki/Wikip%C3%A9dia:V" class="mw-redirect" title="Wikipédia:V">não cobrem</a> todo o conteúdo</b>.<span class="hide-when-compact"> Ajude a <a href="/wiki/Wikip%C3%A9dia:Livro_de_estilo/Refer%C3%AAncias_e_notas_de_rodap%C3%A9" title="Wikipédia:Livro de estilo/Referências e notas de rodapé">inserir referências</a> (<small><i>Encontre fontes:</i> <span class="plainlinks"><a rel="nofollow" class="external text" href="https://wikipedialibrary.wmflabs.org/">ABW</a>  •  <a rel="nofollow" class="external text" href="https://www.periodicos.capes.gov.br">CAPES</a>  •  <a rel="nofollow" class="external text" href="https://www.google.com/search?as_eq=wikipedia&as_epq=Pol%C3%ADgono">Google</a> (<a rel="nofollow" class="external text" href="https://www.google.com/search?hl=pt&tbm=nws&q=Pol%C3%ADgono&oq=Pol%C3%ADgono">N</a> • <a rel="nofollow" class="external text" href="http://books.google.com/books?&as_brr=0&as_epq=Pol%C3%ADgono">L</a> • <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?hl=pt&q=Pol%C3%ADgono">A</a>)</span></small>).</span> <small class="date-container"><i>(<span class="date">Outubro de 2011</span>)</i></small></div></td></tr></tbody></table> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Ficheiro:Complex_polygon.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/34/Complex_polygon.png/220px-Complex_polygon.png" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/34/Complex_polygon.png/330px-Complex_polygon.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/34/Complex_polygon.png/440px-Complex_polygon.png 2x" data-file-width="800" data-file-height="600" /></a><figcaption>Um polígono</figcaption></figure> <p>Em <a href="/wiki/Geometria" title="Geometria">geometria</a>, um <b>polígono</b> é uma figura fechada com lados. A palavra "polígono" vem da palavra em <a href="/wiki/L%C3%ADngua_grega" title="Língua grega">grego</a> "polígonos" que significa ter muitos lados ou ângulos.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span>[</span>1<span>]</span></a></sup> A definição usada por <a href="/wiki/Euclides" title="Euclides">Euclides</a> para polígono era <i>uma figura limitada por linhas retas</i>, sendo que essas linhas deveriam ser mais de quatro, e <i>figura</i> qualquer região do plano cercada por uma ou mais bordas.<sup id="cite_ref-euclides.elementos.1.def.23_2-0" class="reference"><a href="#cite_note-euclides.elementos.1.def.23-2"><span>[</span>2<span>]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Definição"><span id="Defini.C3.A7.C3.A3o"></span>Definição</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pol%C3%ADgono&veaction=edit&section=1" title="Editar secção: Definição" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Pol%C3%ADgono&action=edit&section=1" title="Editar código-fonte da secção: Definição"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/Ficheiro:Linha_poligonal_aberta_simples.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Linha_poligonal_aberta_simples.JPG/220px-Linha_poligonal_aberta_simples.JPG" decoding="async" width="220" height="149" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/9/99/Linha_poligonal_aberta_simples.JPG 1.5x" data-file-width="257" data-file-height="174" /></a><figcaption>Linha poligonal aberta simples</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Linha_poligonal">Linha poligonal</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pol%C3%ADgono&veaction=edit&section=2" title="Editar secção: Linha poligonal" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Pol%C3%ADgono&action=edit&section=2" title="Editar código-fonte da secção: Linha poligonal"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Ficheiro:Linha_poligonal_aberta_n%C3%A3o_simples.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/01/Linha_poligonal_aberta_n%C3%A3o_simples.JPG/220px-Linha_poligonal_aberta_n%C3%A3o_simples.JPG" decoding="async" width="220" height="149" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/0/01/Linha_poligonal_aberta_n%C3%A3o_simples.JPG 1.5x" data-file-width="257" data-file-height="174" /></a><figcaption>Linha poligonal aberta não-simples</figcaption></figure><p>Linha poligonal é uma sucessão de <a href="/wiki/Segmento_de_reta" class="mw-redirect" title="Segmento de reta">segmentos</a> consecutivos e não-colineares, dois a dois. Denotamos uma linha poligonal fornecendo a sequência dos pontos extremos dos segmentos que a formam. Ou seja, a linha poligonal <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_{1}A_{2}A_{3}\cdots A_{n-1}A_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>⋯</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{1}A_{2}A_{3}\cdots A_{n-1}A_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c1dbd94939f61c12a97bc0fd43e2f22f6bd5e99c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:19.913ex; height:2.509ex;" alt="{\displaystyle A_{1}A_{2}A_{3}\cdots A_{n-1}A_{n}}"></span> corresponde a <a href="/wiki/Uni%C3%A3o_(matem%C3%A1tica)" title="União (matemática)">reunião</a> dos segmentos <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 {\overline {A_{1}A_{2}}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mo accent="false">¯</mo> </mover> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {A_{1}A_{2}}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2d459112fe030c687ada4b212df96c7af71c6314" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.356ex; height:3.343ex;" alt="{\displaystyle {\overline {A_{1}A_{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 {\overline {A_{2}A_{3}}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> <mo accent="false">¯</mo> </mover> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {A_{2}A_{3}}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7e8c237c7de331fb896265ca59d32d6dfc434fcd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.356ex; height:3.343ex;" alt="{\displaystyle {\overline {A_{2}A_{3}}},}"></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 {\overline {A_{n-1}A_{n}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mo accent="false">¯</mo> </mover> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {A_{n-1}A_{n}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9098e3004786cb6ec37cfadd04cc115734a616d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.785ex; height:3.343ex;" alt="{\displaystyle {\overline {A_{n-1}A_{n}}}.}"></span><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span>[</span>3<span>]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span>[</span>4<span>]</span></a></sup> </p><div class="mw-heading mw-heading4"><h4 id="Classificação"><span id="Classifica.C3.A7.C3.A3o"></span>Classificação</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pol%C3%ADgono&veaction=edit&section=3" title="Editar secção: Classificação" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Pol%C3%ADgono&action=edit&section=3" title="Editar código-fonte da secção: Classificação"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Uma linha poligonal <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_{1}A_{2}A_{3}\cdots A_{n-1}A_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>⋯</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{1}A_{2}A_{3}\cdots A_{n-1}A_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c1dbd94939f61c12a97bc0fd43e2f22f6bd5e99c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:19.913ex; height:2.509ex;" alt="{\displaystyle A_{1}A_{2}A_{3}\cdots A_{n-1}A_{n}}"></span> é classificada em: </p> <ul><li>aberta - quando os extremos <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_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6bc2435b217c1a0f46f8a517ffa225c6f9440e81" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.797ex; height:2.509ex;" alt="{\displaystyle A_{1}}"></span> e <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_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/730f6906700685b6d52f3958b1c2ae659d2d97d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.962ex; height:2.509ex;" alt="{\displaystyle A_{n}}"></span> não coincidem;</li> <li>fechada - quando os extremos <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_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6bc2435b217c1a0f46f8a517ffa225c6f9440e81" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.797ex; height:2.509ex;" alt="{\displaystyle A_{1}}"></span> e <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_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/730f6906700685b6d52f3958b1c2ae659d2d97d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.962ex; height:2.509ex;" alt="{\displaystyle A_{n}}"></span> coincidem;</li> <li>simples - quando a <a href="/wiki/Interse%C3%A7%C3%A3o" title="Interseção">interseção</a> de qualquer dois segmentos não consecutivos é <a href="/wiki/Conjunto_vazio" title="Conjunto vazio">vazia</a>;</li> <li>não-simples - quando não é simples.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Polígono"><span id="Pol.C3.ADgono"></span>Polígono</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pol%C3%ADgono&veaction=edit&section=4" title="Editar secção: Polígono" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Pol%C3%ADgono&action=edit&section=4" title="Editar código-fonte da secção: Polígono"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Ficheiro:Polygon_definition.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/88/Polygon_definition.png/220px-Polygon_definition.png" decoding="async" width="220" height="169" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/8/88/Polygon_definition.png 1.5x" data-file-width="322" data-file-height="248" /></a><figcaption>Um polígono <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_{1}A_{2}A_{3}\cdots A_{n-1}A_{n}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>⋯</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{1}A_{2}A_{3}\cdots A_{n-1}A_{n}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92659d7e40640560934b390df96a76791ad4ecff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:20.56ex; height:2.509ex;" alt="{\displaystyle A_{1}A_{2}A_{3}\cdots A_{n-1}A_{n}.}"></span> As linhas tracejadas indicam os vários segmentos que o polígono pode ter.</figcaption></figure> <p>Polígono é a região plana limitada por uma linha poligonal fechada. Denotamos um polígono de forma similar a que denotamos uma linha poligonal. Isto é, um polígono <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_{1}A_{2}A_{3}\cdots A_{n-1}A_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>⋯</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{1}A_{2}A_{3}\cdots A_{n-1}A_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c1dbd94939f61c12a97bc0fd43e2f22f6bd5e99c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:19.913ex; height:2.509ex;" alt="{\displaystyle A_{1}A_{2}A_{3}\cdots A_{n-1}A_{n}}"></span> corresponde à região limitada pela reunião dos segmentos <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 {\overline {A_{1}A_{2}}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mo accent="false">¯</mo> </mover> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {A_{1}A_{2}}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2d459112fe030c687ada4b212df96c7af71c6314" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.356ex; height:3.343ex;" alt="{\displaystyle {\overline {A_{1}A_{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 {\overline {A_{2}A_{3}}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> <mo accent="false">¯</mo> </mover> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {A_{2}A_{3}}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7e8c237c7de331fb896265ca59d32d6dfc434fcd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.356ex; height:3.343ex;" alt="{\displaystyle {\overline {A_{2}A_{3}}},}"></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 {\overline {A_{n-1}A_{n}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mo accent="false">¯</mo> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {A_{n-1}A_{n}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/60d2326c839355325ca8f6234191adf0638e9321" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.139ex; height:3.343ex;" alt="{\displaystyle {\overline {A_{n-1}A_{n}}}}"></span> e <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 {\overline {A_{n}A_{1}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mo accent="false">¯</mo> </mover> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {A_{n}A_{1}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b9dc11a23d4c0ef0240dab1b5fd334f5e8284c8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.521ex; height:3.343ex;" alt="{\displaystyle {\overline {A_{n}A_{1}}}.}"></span> <sup id="cite_ref-:0_5-0" class="reference"><a href="#cite_note-:0-5"><span>[</span>5<span>]</span></a></sup> </p><p>Na literatura, também encontramos o termo polígono como sinônimo de linha poligonal fechada. Neste caso, a região plana limitada pelo polígono é chamada de seu interior e a união do polígono com seu interior é chamada de <b>região poligonal</b> ou <b>superfície poligonal</b>.<sup id="cite_ref-:0_5-1" class="reference"><a href="#cite_note-:0-5"><span>[</span>5<span>]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Elementos">Elementos</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pol%C3%ADgono&veaction=edit&section=5" title="Editar secção: Elementos" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Pol%C3%ADgono&action=edit&section=5" title="Editar código-fonte da secção: Elementos"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Um polígono <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_{1}A_{2}A_{3}\cdots A_{n-1}A_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>⋯</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{1}A_{2}A_{3}\cdots A_{n-1}A_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c1dbd94939f61c12a97bc0fd43e2f22f6bd5e99c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:19.913ex; height:2.509ex;" alt="{\displaystyle A_{1}A_{2}A_{3}\cdots A_{n-1}A_{n}}"></span> possui os seguintes elementos:<sup id="cite_ref-:0_5-2" class="reference"><a href="#cite_note-:0-5"><span>[</span>5<span>]</span></a></sup> </p> <ul><li><a href="/wiki/V%C3%A9rtice" title="Vértice">vértice</a> - extremo de um dos segmentos que formam o polígono, i.e. são vértices os pontos <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_{1},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{1},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eaac19dd9a383457a52222837be415c8b1354909" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.444ex; height:2.509ex;" alt="{\displaystyle A_{1},}"></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 A_{2},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{2},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6a01dea03d426ee6e3efd7978055e7cce45ca779" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.444ex; height:2.509ex;" alt="{\displaystyle A_{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 A_{3},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{3},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/808e5ffc03d576ce7235372adbdd7476b0e549f7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.444ex; height:2.509ex;" alt="{\displaystyle A_{3},}"></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 A_{n};}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>;</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{n};}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3aca94bae26acf2ae6de6cec535b76f9981d7efa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.608ex; height:2.509ex;" alt="{\displaystyle A_{n};}"></span></li> <li>lado - segmento que forma o polígono, i.e. são lados os segmentos <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 {\overline {A_{1}A_{2}}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mo accent="false">¯</mo> </mover> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {A_{1}A_{2}}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2d459112fe030c687ada4b212df96c7af71c6314" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.356ex; height:3.343ex;" alt="{\displaystyle {\overline {A_{1}A_{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 {\overline {A_{2}A_{3}}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> <mo accent="false">¯</mo> </mover> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {A_{2}A_{3}}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7e8c237c7de331fb896265ca59d32d6dfc434fcd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.356ex; height:3.343ex;" alt="{\displaystyle {\overline {A_{2}A_{3}}},}"></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 {\overline {A_{n-1}A_{n}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mo accent="false">¯</mo> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {A_{n-1}A_{n}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/60d2326c839355325ca8f6234191adf0638e9321" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.139ex; height:3.343ex;" alt="{\displaystyle {\overline {A_{n-1}A_{n}}}}"></span> e <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 {\overline {A_{n}A_{1}}};}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mo accent="false">¯</mo> </mover> </mrow> <mo>;</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {A_{n}A_{1}}};}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5dc17be7bf27e029953cf7d158c18ad0349f4a90" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.521ex; height:3.343ex;" alt="{\displaystyle {\overline {A_{n}A_{1}}};}"></span></li> <li><a href="/wiki/Diagonais_de_um_pol%C3%ADgono" title="Diagonais de um polígono">diagonais</a> - segmentos de reta com extremidades em vértices não consecutivos;</li> <li><a href="/wiki/%C3%82ngulo" title="Ângulo">ângulo</a> (interno) - ângulo formado por dois lados consecutivos, i.e. os ângulos <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {A}}_{1}=A_{n}{\hat {A}}_{1}A_{2},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {A}}_{1}=A_{n}{\hat {A}}_{1}A_{2},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/19cd4ea3ddf8a494adf75de04194adb939c2872a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.164ex; height:3.176ex;" alt="{\displaystyle {\hat {A}}_{1}=A_{n}{\hat {A}}_{1}A_{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 {\hat {A}}_{2}=A_{1}{\hat {A}}_{2}A_{3},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {A}}_{2}=A_{1}{\hat {A}}_{2}A_{3},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3a493fd440bd8006947167404db7192cec5635b1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15ex; height:3.176ex;" alt="{\displaystyle {\hat {A}}_{2}=A_{1}{\hat {A}}_{2}A_{3},}"></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 {\hat {A}}_{n}=A_{n-1}{\hat {A}}_{n}A_{1};}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>;</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {A}}_{n}=A_{n-1}{\hat {A}}_{n}A_{1};}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e5f7bf23b4a98c090ac3faf1b510b545c945608a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:17.593ex; height:3.176ex;" alt="{\displaystyle {\hat {A}}_{n}=A_{n-1}{\hat {A}}_{n}A_{1};}"></span></li> <li>ângulo externo - ângulo suplementar e adjacente a um ângulo interno.</li></ul> <figure class="mw-default-size mw-halign-right" typeof="mw:File"><a href="/wiki/Ficheiro:Pentagono_regular_e_seus_elementos.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/06/Pentagono_regular_e_seus_elementos.svg/224px-Pentagono_regular_e_seus_elementos.svg.png" decoding="async" width="224" height="226" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/06/Pentagono_regular_e_seus_elementos.svg/336px-Pentagono_regular_e_seus_elementos.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/06/Pentagono_regular_e_seus_elementos.svg/448px-Pentagono_regular_e_seus_elementos.svg.png 2x" data-file-width="224" data-file-height="226" /></a><figcaption></figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Exemplo">Exemplo</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pol%C3%ADgono&veaction=edit&section=6" title="Editar secção: Exemplo" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Pol%C3%ADgono&action=edit&section=6" title="Editar código-fonte da secção: Exemplo"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>O polígono <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 ABCDE}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mi>B</mi> <mi>C</mi> <mi>D</mi> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ABCDE}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e159ba4f32a6bd3a6b8467c293f7ed9994acf32c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.973ex; height:2.176ex;" alt="{\displaystyle ABCDE}"></span> na figura ao lado possui: </p> <ul><li>vértices <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> <mo>,</mo> </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/2746026864cc5896e3e52443a1c917be2df9d8ea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.39ex; height:2.509ex;" alt="{\displaystyle A,}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mo>,</mo> </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/075d661417b8ca5a991a2a7bd4991cc1ab856d9d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.411ex; height:2.509ex;" alt="{\displaystyle B,}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mo>,</mo> </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/64528f031cdbe1f52bdaf4ba7a8401108c0d2dc2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.413ex; height:2.509ex;" alt="{\displaystyle C,}"></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 D,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> <mo>,</mo> </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/ab9cb9bd7fcb5f2a543b128c1b876019b158c0fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.571ex; height:2.509ex;" alt="{\displaystyle D,}"></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 E;}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>;</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E;}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8a7c83e9dddd33420cdf857a5747b4cfc47db191" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.422ex; height:2.509ex;" alt="{\displaystyle E;}"></span></li> <li>lados <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 {\overline {AB}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>A</mi> <mi>B</mi> </mrow> <mo accent="false">¯</mo> </mover> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {AB}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1edf91b56517db990b51163da55f0341158a4fb4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.269ex; height:3.343ex;" alt="{\displaystyle {\overline {AB}},}"></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 {\overline {BC}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>B</mi> <mi>C</mi> </mrow> <mo accent="false">¯</mo> </mover> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {BC}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c1afbd02bc55f4af75f672737158ab9c3387f166" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.36ex; height:3.343ex;" alt="{\displaystyle {\overline {BC}},}"></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 {\overline {CD}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>C</mi> <mi>D</mi> </mrow> <mo accent="false">¯</mo> </mover> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {CD}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d528c0e913f15d3274b7db8bd7d74da6e46d2c83" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.452ex; height:3.343ex;" alt="{\displaystyle {\overline {CD}},}"></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 {\overline {DE}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>D</mi> <mi>E</mi> </mrow> <mo accent="false">¯</mo> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {DE}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a4fcfc4373cde19c969df60998941ce1e27ac57" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.854ex; height:3.009ex;" alt="{\displaystyle {\overline {DE}}}"></span> e <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 {\overline {EA}};}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>E</mi> <mi>A</mi> </mrow> <mo accent="false">¯</mo> </mover> </mrow> <mo>;</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {EA}};}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4ab930e5d0ba1b94672fb0ed6e20d8048786905e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.281ex; height:3.343ex;" alt="{\displaystyle {\overline {EA}};}"></span></li> <li>ângulos internos <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {a}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {a}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d5d70cc3665c6270422020db544808ac5abe26fe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.877ex; height:2.509ex;" alt="{\displaystyle {\hat {a}},}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {b}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>b</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {b}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d287de5f7242e0c1d5a8cdf57a66ea0f675b5d4e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.809ex; height:3.176ex;" alt="{\displaystyle {\hat {b}},}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {c}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>c</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {c}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/efdf369d108dc999834a77d3168de9111f0facd3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.938ex; height:2.509ex;" alt="{\displaystyle {\hat {c}},}"></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 {\hat {d}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>d</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {d}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1091bf45bb6d29dc63143fb4299c0dd90156b528" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.228ex; height:3.176ex;" alt="{\displaystyle {\hat {d}},}"></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 {\hat {e}};}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>e</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo>;</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {e}};}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7caa21213960264000c9717a7c671c38e9d92f40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.938ex; height:2.509ex;" alt="{\displaystyle {\hat {e}};}"></span></li> <li>diagonais <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 {\overline {AC}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>A</mi> <mi>C</mi> </mrow> <mo accent="false">¯</mo> </mover> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {AC}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/355157afd115892d4f07b369140eae38aca63888" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.339ex; height:3.343ex;" alt="{\displaystyle {\overline {AC}},}"></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 {\overline {AD}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>A</mi> <mi>D</mi> </mrow> <mo accent="false">¯</mo> </mover> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {AD}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/899b933fe907d6fad70036cd2ef3ff59b2c56c6c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.429ex; height:3.343ex;" alt="{\displaystyle {\overline {AD}},}"></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 {\overline {BD}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>B</mi> <mi>D</mi> </mrow> <mo accent="false">¯</mo> </mover> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {BD}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/51bafb65b8aebf4d74ce4380d0926ddfcb93bf58" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.45ex; height:3.343ex;" alt="{\displaystyle {\overline {BD}},}"></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 {\overline {BE}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>B</mi> <mi>E</mi> </mrow> <mo accent="false">¯</mo> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {BE}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92eaba64d81078d81da3d2ccb9fe9aea31f728f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.694ex; height:3.009ex;" alt="{\displaystyle {\overline {BE}}}"></span> e <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 {\overline {CE}};}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>C</mi> <mi>E</mi> </mrow> <mo accent="false">¯</mo> </mover> </mrow> <mo>;</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {CE}};}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1daa040219ae73ae4eb207ad99430113760a4705" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.343ex; height:3.343ex;" alt="{\displaystyle {\overline {CE}};}"></span></li> <li>ângulos externos <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {a}}_{1},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {a}}_{1},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ecfe9962112baa029f4e786c5ba83be011ec0f7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.931ex; height:2.509ex;" alt="{\displaystyle {\hat {a}}_{1},}"></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 {\hat {b}}_{1},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>b</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {b}}_{1},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a94731c3b44ba9b39112fe765f899a699f089967" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.864ex; height:3.176ex;" alt="{\displaystyle {\hat {b}}_{1},}"></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 {\hat {c}}_{1},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>c</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {c}}_{1},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d25bf6fdc536d227eb0f9c5de1802d8677b62f2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.993ex; height:2.509ex;" alt="{\displaystyle {\hat {c}}_{1},}"></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 {\hat {d}}_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>d</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {d}}_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/50b6409b4556f13330e71bc3898e1245fcc2a124" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.636ex; height:3.176ex;" alt="{\displaystyle {\hat {d}}_{1}}"></span> e <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {e}}_{1}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>e</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {e}}_{1}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/80ae3136a87d14b58ec2ba376feabde99c189aae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.993ex; height:2.509ex;" alt="{\displaystyle {\hat {e}}_{1}.}"></span></li></ul> <div class="mw-heading mw-heading3"><h3 id="Perímetro_e_Área"><span id="Per.C3.ADmetro_e_.C3.81rea"></span>Perímetro e Área</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pol%C3%ADgono&veaction=edit&section=7" title="Editar secção: Perímetro e Área" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Pol%C3%ADgono&action=edit&section=7" title="Editar código-fonte da secção: Perímetro e Área"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>O perímetro de um polígono é a soma das medidas de seus lados. Sua área é a medida da região poligonal definida pelo polígono. </p> <div class="mw-heading mw-heading2"><h2 id="Classificação_2"><span id="Classifica.C3.A7.C3.A3o_2"></span>Classificação</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pol%C3%ADgono&veaction=edit&section=8" title="Editar secção: Classificação" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Pol%C3%ADgono&action=edit&section=8" title="Editar código-fonte da secção: Classificação"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Ficheiro:Polygon_types_in_Portuguese.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/26/Polygon_types_in_Portuguese.svg/300px-Polygon_types_in_Portuguese.svg.png" decoding="async" width="300" height="248" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/26/Polygon_types_in_Portuguese.svg/450px-Polygon_types_in_Portuguese.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/26/Polygon_types_in_Portuguese.svg/600px-Polygon_types_in_Portuguese.svg.png 2x" data-file-width="728" data-file-height="601" /></a><figcaption>Diferentes tipos de polígonos</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Quanto_à_linha_poligonal"><span id="Quanto_.C3.A0_linha_poligonal"></span>Quanto à linha poligonal</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pol%C3%ADgono&veaction=edit&section=9" title="Editar secção: Quanto à linha poligonal" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Pol%C3%ADgono&action=edit&section=9" title="Editar código-fonte da secção: Quanto à linha poligonal"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Um polígono <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_{1}A_{2}A_{3}\cdots A_{n-1}A_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>⋯</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{1}A_{2}A_{3}\cdots A_{n-1}A_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c1dbd94939f61c12a97bc0fd43e2f22f6bd5e99c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:19.913ex; height:2.509ex;" alt="{\displaystyle A_{1}A_{2}A_{3}\cdots A_{n-1}A_{n}}"></span> pode ser classificado em simples, quando sua linha poligonal associada é simples, ou não-simples (ou complexo), quando sua linha poligonal tem cruzamentos entre seus segmentos (conjunto intersecção não-nulo).<sup id="cite_ref-:0_5-3" class="reference"><a href="#cite_note-:0-5"><span>[</span>5<span>]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Quanto_à_região_poligonal"><span id="Quanto_.C3.A0_regi.C3.A3o_poligonal"></span>Quanto à região poligonal</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pol%C3%ADgono&veaction=edit&section=10" title="Editar secção: Quanto à região poligonal" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Pol%C3%ADgono&action=edit&section=10" title="Editar código-fonte da secção: Quanto à região poligonal"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Um polígono simples é dito ser <a href="/wiki/Conjunto_convexo" title="Conjunto convexo">convexo</a> quando toda reta determinada por dois de seus vértices consecutivos faz com que todos os demais vértices estejam num mesmo <a href="/wiki/Semiplano" title="Semiplano">semiplano</a> determinado por ela. Um polígono que não é convexo é dito ser côncavo.<sup id="cite_ref-:0_5-4" class="reference"><a href="#cite_note-:0-5"><span>[</span>5<span>]</span></a></sup> Polígonos estrelados são polígonos complexos cujas intersecções de segmentos são equidistantes entre si.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span>[</span>6<span>]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Quanto_à_congruência"><span id="Quanto_.C3.A0_congru.C3.AAncia"></span>Quanto à congruência</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pol%C3%ADgono&veaction=edit&section=11" title="Editar secção: Quanto à congruência" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Pol%C3%ADgono&action=edit&section=11" title="Editar código-fonte da secção: Quanto à congruência"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Um polígono é dito ser <b>equilátero</b> quando todos os seus lados são <a href="/wiki/Congru%C3%AAncia_(geometria)" title="Congruência (geometria)">congruentes</a>. Similarmente, é dito ser <b>equiângulo</b> quando todos os seus ângulos são congruentes. Polígonos convexos equiláteros e equiângulos são chamados de <b>polígonos regulares</b>. </p> <div class="mw-heading mw-heading3"><h3 id="Quanto_ao_número_de_lados"><span id="Quanto_ao_n.C3.BAmero_de_lados"></span>Quanto ao número de lados</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pol%C3%ADgono&veaction=edit&section=12" title="Editar secção: Quanto ao número de lados" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Pol%C3%ADgono&action=edit&section=12" title="Editar código-fonte da secção: Quanto ao número de lados"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="hatnote"><span typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Disambig_grey.svg/20px-Disambig_grey.svg.png" decoding="async" width="20" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Disambig_grey.svg/30px-Disambig_grey.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Disambig_grey.svg/40px-Disambig_grey.svg.png 2x" data-file-width="260" data-file-height="200" /></span></span> <b>Nota:</b> "Pentágono" redireciona para este artigo. Para outros significados, veja <a href="/wiki/Pent%C3%A1gono_(desambigua%C3%A7%C3%A3o)" class="mw-disambig" title="Pentágono (desambiguação)">Pentágono (desambiguação)</a>.</div> <p>Os polígonos também são classificados quanto ao número de lados. Em geral, um polígono de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> lados é chamado de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span>-látero. Entretanto, comumente empregam-se as seguintes nomenclaturas:<sup id="cite_ref-:0_5-5" class="reference"><a href="#cite_note-:0-5"><span>[</span>5<span>]</span></a></sup> </p> <table class="wikitable"> <caption>Nomes dos polígonos </caption> <tbody><tr> <th>Lados</th> <th>Nome</th> <th>Lados</th> <th>Nome</th> <th>Lados</th> <th>Nome </th></tr> <tr> <td>1</td> <td>não existe</td> <td>11</td> <td>undecágono</td> <td rowspan="2" style="text-align:center;">...</td> <td rowspan="2" style="text-align:center;">... </td></tr> <tr> <td>2</td> <td>não existe</td> <td>12</td> <td>dodecágono </td></tr> <tr> <td>3</td> <td><a href="/wiki/Tri%C3%A2ngulo" title="Triângulo">triângulo</a> ou trilátero</td> <td>13</td> <td>tridecágono</td> <td>30</td> <td><a href="/wiki/Triacont%C3%A1gono" title="Triacontágono">triacontágono</a> </td></tr> <tr> <td>4</td> <td><a href="/wiki/Quadril%C3%A1tero" title="Quadrilátero">quadrilátero</a></td> <td>14</td> <td>tetradecágono</td> <td>40</td> <td><a href="/wiki/Tetracont%C3%A1gono" title="Tetracontágono">tetracontágono</a> </td></tr> <tr> <td>5</td> <td>pentágono</td> <td>15</td> <td>pentadecágono</td> <td>50</td> <td>pentacontágono </td></tr> <tr> <td>6</td> <td>hexágono</td> <td>16</td> <td>hexadecágono</td> <td>60</td> <td>hexacontágono </td></tr> <tr> <td>7</td> <td><a href="/wiki/Hept%C3%A1gono" title="Heptágono">heptágono</a></td> <td>17</td> <td><a href="/wiki/Heptadec%C3%A1gono" title="Heptadecágono">heptadecágono</a></td> <td>70</td> <td>heptacontágono </td></tr> <tr> <td>8</td> <td><a href="/wiki/Oct%C3%B3gono" title="Octógono">octógono</a></td> <td>18</td> <td><a href="/wiki/Octodec%C3%A1gono" title="Octodecágono">octodecágono</a></td> <td>80</td> <td>octacontágono </td></tr> <tr> <td>9</td> <td>eneágono</td> <td>19</td> <td>eneadecágono</td> <td>90</td> <td>eneacontágono </td></tr> <tr> <td>10</td> <td>decágono</td> <td>20</td> <td>icoságono</td> <td>100</td> <td>hectágono </td></tr> </tbody></table> <div class="mw-heading mw-heading4"><h4 id="Nomenclatura_para_polígonos_com_muitos_lados"><span id="Nomenclatura_para_pol.C3.ADgonos_com_muitos_lados"></span>Nomenclatura para polígonos com muitos lados</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pol%C3%ADgono&veaction=edit&section=13" title="Editar secção: Nomenclatura para polígonos com muitos lados" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Pol%C3%ADgono&action=edit&section=13" title="Editar código-fonte da secção: Nomenclatura para polígonos com muitos lados"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Para se construir o nome de um polígono com mais de 20 lados e menos de 100 lados, basta se combinar os prefixos e os sufixos a seguir:<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span>[</span>7<span>]</span></a></sup> </p> <table class="wikitable" style="vertical-align:center;"> <tbody><tr style="text-align:center;"> <th colspan="2" rowspan="2">Dezenas </th> <th><i>e</i> </th> <th colspan="2">Unidades </th> <th>sufixo </th></tr> <tr> <th rowspan="9">-cai- </th> <td>1 </td> <td>-ena- </td> <th rowspan="9">-gono </th></tr> <tr> <td><b>20</b></td> <td>icosi-</td> <td>2</td> <td>-di- </td></tr> <tr> <td><b>30</b></td> <td>triaconta-</td> <td>3</td> <td>-tri- </td></tr> <tr> <td><b>40</b></td> <td>tetraconta-</td> <td>4</td> <td>-tetra- </td></tr> <tr> <td><b>50</b></td> <td>pentaconta-</td> <td>5</td> <td>-penta- </td></tr> <tr> <td><b>60</b></td> <td>hexaconta-</td> <td>6</td> <td>-hexa- </td></tr> <tr> <td><b>70</b></td> <td>heptaconta-</td> <td>7</td> <td>-hepta- </td></tr> <tr> <td><b>80</b></td> <td>octaconta-</td> <td>8</td> <td>-octa- </td></tr> <tr> <td><b>90</b></td> <td>eneaconta-</td> <td>9</td> <td>-enea- </td></tr> </tbody></table> <div class="mw-heading mw-heading5"><h5 id="Exemplo_1">Exemplo 1</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pol%C3%ADgono&veaction=edit&section=14" title="Editar secção: Exemplo 1" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Pol%C3%ADgono&action=edit&section=14" title="Editar código-fonte da secção: Exemplo 1"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Um polígono de 42 lados deve ser nomeado da seguinte maneira: </p> <table class="wikitable"> <tbody><tr> <th>Dezenas </th> <th><i>e</i> </th> <th>Unidades </th> <th>sufixo </th> <th>nome completo do polígono </th></tr> <tr> <td>tetraconta- </td> <td>-cai- </td> <td>-di- </td> <td>-gono </td> <td>tetracontacaidígono </td></tr> </tbody></table> <div class="mw-heading mw-heading5"><h5 id="Exemplo_2">Exemplo 2</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pol%C3%ADgono&veaction=edit&section=15" title="Editar secção: Exemplo 2" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Pol%C3%ADgono&action=edit&section=15" title="Editar código-fonte da secção: Exemplo 2"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Um polígono de 50 lados da seguinte forma: </p> <table class="wikitable"> <tbody><tr> <th>Dezenas </th> <th><i>e</i> </th> <th>Unidades </th> <th>sufixo </th> <th>nome completo do polígono </th></tr> <tr> <td>pentaconta- </td> <td colspan="2">  </td> <td>-gono </td> <td>pentacontágono </td></tr> </tbody></table> <p>Alguns polígonos possuem nomes alternativos, como o miriágono (10.000 lados).<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span>[</span>8<span>]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Propriedades">Propriedades</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pol%C3%ADgono&veaction=edit&section=16" title="Editar secção: Propriedades" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Pol%C3%ADgono&action=edit&section=16" title="Editar código-fonte da secção: Propriedades"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Podemos observar uma série de relações entre os diversos elementos de um polígono.<sup id="cite_ref-:0_5-6" class="reference"><a href="#cite_note-:0-5"><span>[</span>5<span>]</span></a></sup> Aqui, apresentamos algumas destas propriedades. </p> <div class="mw-heading mw-heading3"><h3 id="Vértices_e_lados"><span id="V.C3.A9rtices_e_lados"></span>Vértices e lados</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pol%C3%ADgono&veaction=edit&section=17" title="Editar secção: Vértices e lados" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Pol%C3%ADgono&action=edit&section=17" title="Editar código-fonte da secção: Vértices e lados"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>O número de lados e o número de ângulos de um polígono é igual ao seu número de vértices. </p> <div class="mw-heading mw-heading3"><h3 id="Diagonais">Diagonais</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pol%C3%ADgono&veaction=edit&section=18" title="Editar secção: Diagonais" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Pol%C3%ADgono&action=edit&section=18" title="Editar código-fonte da secção: Diagonais"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>De cada vértice de um polígono de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> lados, saem <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n-3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>−</mo> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n-3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3ee3741ee7dd3d098f3f16980e15c0435471dda0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.398ex; height:2.343ex;" alt="{\displaystyle n-3}"></span> diagonais. Com efeito, um polígono de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> lados tem <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> vértices. De um dado vértice formamos <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n-1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n-1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fbd0b0f32b28f51962943ee9ede4fb34198a2521" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.398ex; height:2.343ex;" alt="{\displaystyle n-1}"></span> segmentos de reta com cada um dos outros <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n-1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n-1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fbd0b0f32b28f51962943ee9ede4fb34198a2521" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.398ex; height:2.343ex;" alt="{\displaystyle n-1}"></span> vértices. Agora, observamos que dois destes segmentos são lados do polígono, portanto, de cada vértice partem <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n-3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>−</mo> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n-3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3ee3741ee7dd3d098f3f16980e15c0435471dda0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.398ex; height:2.343ex;" alt="{\displaystyle n-3}"></span> diagonais.</li> <li>O número de diagonais <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> </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/e85ff03cbe0c7341af6b982e47e9f90d235c66ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.216ex; height:2.176ex;" alt="{\displaystyle d}"></span> de um polígono <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span>-látero é: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d={\frac {n(n-3)}{2}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>n</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d={\frac {n(n-3)}{2}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8fa90484081d60e1a9e594d9065013eb352a699" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:14.399ex; height:5.676ex;" alt="{\displaystyle d={\frac {n(n-3)}{2}}.}"></span> Com efeito, a <a href="/wiki/Combina%C3%A7%C3%A3o_(matem%C3%A1tica)" class="mw-redirect" title="Combinação (matemática)">combinação</a> de seus <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> vértices dois a dois fornece o número total de segmentos de reta que podem ser construídos usando todos os seus vértices. Deste número, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> são lados do polígono e o restante são diagonais, i.e.: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d=C_{s}^{n}-n={\frac {n!}{2!(n-2)!}}-n={\frac {n(n-1)}{2}}-n={\frac {n(n-3)}{2}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo>=</mo> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msubsup> <mo>−</mo> <mi>n</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>n</mi> <mo>!</mo> </mrow> <mrow> <mn>2</mn> <mo>!</mo> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>!</mo> </mrow> </mfrac> </mrow> <mo>−</mo> <mi>n</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>n</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>−</mo> <mi>n</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>n</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d=C_{s}^{n}-n={\frac {n!}{2!(n-2)!}}-n={\frac {n(n-1)}{2}}-n={\frac {n(n-3)}{2}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5dacedd2428b3ad834ccbfc0fca58f7c7ef6fcba" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:59.353ex; height:6.509ex;" alt="{\displaystyle d=C_{s}^{n}-n={\frac {n!}{2!(n-2)!}}-n={\frac {n(n-1)}{2}}-n={\frac {n(n-3)}{2}}.}"></span></li> <li>Em um polígono convexo de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> lados, o número de triângulos formados por diagonais que saem de cada vértice é dado por <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n-2.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>−</mo> <mn>2.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n-2.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a4ba9c2616dae66b1e9f4f59300e6ee52debc4d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:6.044ex; height:2.343ex;" alt="{\displaystyle n-2.}"></span> De fato, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n-3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>−</mo> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n-3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3ee3741ee7dd3d098f3f16980e15c0435471dda0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.398ex; height:2.343ex;" alt="{\displaystyle n-3}"></span> diagonais partem de cada vértice determinando, com os lados do polígono, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n-2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>−</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n-2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ff40d66ad535411eedb9c686a9008a5089c35ac0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.398ex; height:2.343ex;" alt="{\displaystyle n-2}"></span> triângulos.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Ângulos"><span id=".C3.82ngulos"></span>Ângulos</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pol%C3%ADgono&veaction=edit&section=19" title="Editar secção: Ângulos" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Pol%C3%ADgono&action=edit&section=19" title="Editar código-fonte da secção: Ângulos"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>A soma das medidas dos ângulos internos <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 S_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de6e810a93f67802ecb603ee0e3324005c6e583e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.225ex; height:2.509ex;" alt="{\displaystyle S_{i}}"></span> de um polígono convexo de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> lados é dada por: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{i}=(n-2)\cdot 180^{\circ }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>⋅</mo> <msup> <mn>180</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{i}=(n-2)\cdot 180^{\circ }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53c11e17582072a1240fb836c1433179a98a0fcc" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.751ex; height:2.843ex;" alt="{\displaystyle S_{i}=(n-2)\cdot 180^{\circ }}"></span> Com efeito, as diagonais que partem de um dado vértice formam <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n-2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>−</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n-2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ff40d66ad535411eedb9c686a9008a5089c35ac0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.398ex; height:2.343ex;" alt="{\displaystyle n-2}"></span> triângulos. Observamos que <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 S_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de6e810a93f67802ecb603ee0e3324005c6e583e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.225ex; height:2.509ex;" alt="{\displaystyle S_{i}}"></span> é igual a soma dos ângulos internos destes <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n-2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>−</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n-2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ff40d66ad535411eedb9c686a9008a5089c35ac0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.398ex; height:2.343ex;" alt="{\displaystyle n-2}"></span> triângulos, i.e. <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 S_{i}=(n-2)\cdot 180^{\circ }.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>⋅</mo> <msup> <mn>180</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{i}=(n-2)\cdot 180^{\circ }.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/333aea59585c6937f8284c350d5068009feefc38" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.397ex; height:2.843ex;" alt="{\displaystyle S_{i}=(n-2)\cdot 180^{\circ }.}"></span></li> <li>A soma das medidas dos ângulos externos <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 S_{e}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{e}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c116b38a936976c554aaf49bddf5c6476313dab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.423ex; height:2.509ex;" alt="{\displaystyle S_{e}}"></span> de um polígono convexo de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> lados é igual 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 360^{\circ }.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>360</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 360^{\circ }.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/52680a64e3d928c497c21b814679935693a94e8a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.188ex; height:2.343ex;" alt="{\displaystyle 360^{\circ }.}"></span> Com efeito, sejam <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {a}}_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {a}}_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/217faa90f4a1c26d1b6ef135e7b94579f515f9ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.029ex; height:2.509ex;" alt="{\displaystyle {\hat {a}}_{i}}"></span> e <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {b}}_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>b</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {b}}_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/349d7dbe78f35abc9839588ed3b1c5983bfcc4ff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.962ex; height:3.176ex;" alt="{\displaystyle {\hat {b}}_{i}}"></span> os respectivos ângulos interno e externo do <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 i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span>-ésimo vértice de um polígono <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span>-látero. Por definição, temos <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {a}}_{i}+{\hat {b}}_{i}=180^{\circ }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>+</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>b</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msup> <mn>180</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {a}}_{i}+{\hat {b}}_{i}=180^{\circ }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/56ab6309cef58269fa4a632c46f47aaed453c526" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.472ex; height:3.176ex;" alt="{\displaystyle {\hat {a}}_{i}+{\hat {b}}_{i}=180^{\circ }}"></span> para todo <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 i=1,\ldots ,n.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mi>n</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i=1,\ldots ,n.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/df1fdaf4311ca9e5826a22477bcd28ce4b042fcf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.283ex; height:2.509ex;" alt="{\displaystyle i=1,\ldots ,n.}"></span> Daí, segue que: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 180^{\circ }n=\sum _{i=1}^{n}{\hat {a}}_{i}+{\hat {b}}_{i}=S_{i}+S_{e}=180^{\circ }(n-2)+S_{e}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>180</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mi>n</mi> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>+</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>b</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <mo>=</mo> <msup> <mn>180</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>+</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 180^{\circ }n=\sum _{i=1}^{n}{\hat {a}}_{i}+{\hat {b}}_{i}=S_{i}+S_{e}=180^{\circ }(n-2)+S_{e}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/145b30f4d663df08b4f1dc726fafd4742bfb3b66" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:50.306ex; height:6.843ex;" alt="{\displaystyle 180^{\circ }n=\sum _{i=1}^{n}{\hat {a}}_{i}+{\hat {b}}_{i}=S_{i}+S_{e}=180^{\circ }(n-2)+S_{e}}"></span> donde, vemos que <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 S_{e}=360^{\circ }.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <mo>=</mo> <msup> <mn>360</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{e}=360^{\circ }.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7a0ec28d45ba605f586ec3307a0c1e1d8ab7e579" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.71ex; height:2.676ex;" alt="{\displaystyle S_{e}=360^{\circ }.}"></span></li> <li>A medida do ângulo interno <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {a}}_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {a}}_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/217faa90f4a1c26d1b6ef135e7b94579f515f9ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.029ex; height:2.509ex;" alt="{\displaystyle {\hat {a}}_{i}}"></span> de um polígono regular de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> lados é dada por: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {a}}_{i}={\frac {(n-2).180^{\circ }}{n}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>2</mn> <mo stretchy="false">)</mo> <msup> <mn>.180</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mrow> <mi>n</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {a}}_{i}={\frac {(n-2).180^{\circ }}{n}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/daf1204a881dbfa6c8dee737ddffc8bc4b5853f7" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:18.359ex; height:5.676ex;" alt="{\displaystyle {\hat {a}}_{i}={\frac {(n-2).180^{\circ }}{n}}}"></span></li> <li>A medida do ângulo externo <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_{e}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{e}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/98816e68da157c1252b8ac2bdc896cce7636e855" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.228ex; height:2.009ex;" alt="{\displaystyle a_{e}}"></span> de um polígono regular de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> lados é dada por: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{e}={\frac {360^{\circ }}{n}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mn>360</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mi>n</mi> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{e}={\frac {360^{\circ }}{n}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3fd71d64bc3a6e1aff3f86512e9b66d68689d41f" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:11.351ex; height:5.343ex;" alt="{\displaystyle a_{e}={\frac {360^{\circ }}{n}}.}"></span></li> <li>A soma das medidas dos ângulos centrais de um polígono regular de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> lados (<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 S_{c}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{c}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c9f8b4d1ecb693aefb3372c33479d00103085d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.369ex; height:2.509ex;" alt="{\displaystyle S_{c}}"></span>) é igual 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 360^{\circ }.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>360</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 360^{\circ }.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/52680a64e3d928c497c21b814679935693a94e8a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.188ex; height:2.343ex;" alt="{\displaystyle 360^{\circ }.}"></span></li> <li>A medida do ângulo central de um polígono regular de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> lados (<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_{c}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{c}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81c3b8855d2273be442a8cdddc9943fd2af67bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.174ex; height:2.009ex;" alt="{\displaystyle a_{c}}"></span>) é dada por: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{c}={\frac {360^{\circ }}{n}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mn>360</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mi>n</mi> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{c}={\frac {360^{\circ }}{n}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5072fb2432bca13add1488c9d178d3dbdf806495" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:11.297ex; height:5.343ex;" alt="{\displaystyle a_{c}={\frac {360^{\circ }}{n}}.}"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="Mitologia">Mitologia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pol%C3%ADgono&veaction=edit&section=20" title="Editar secção: Mitologia" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Pol%C3%ADgono&action=edit&section=20" title="Editar código-fonte da secção: Mitologia"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Segundo <a href="/wiki/Eudoxo_de_Cnido" title="Eudoxo de Cnido">Eudoxo</a>, citado por <a href="/wiki/Plutarco" title="Plutarco">Plutarco</a>, os <a href="/wiki/Escola_pitag%C3%B3rica" title="Escola pitagórica">pitagóricos</a> associavam cada polígono a um (ou mais) deuses. O triângulo pertencia a <a href="/wiki/Hades" title="Hades">Hades</a>, <a href="/wiki/Dion%C3%ADsio" class="mw-redirect" title="Dionísio">Dionísio</a> e <a href="/wiki/Ares" title="Ares">Ares</a>, o quadrilátero a <a href="/wiki/Reia" title="Reia">Reia</a>, <a href="/wiki/Afrodite" title="Afrodite">Afrodite</a>, <a href="/wiki/Dem%C3%A9ter" title="Deméter">Deméter</a>, <a href="/wiki/H%C3%A9stia" title="Héstia">Héstia</a> e <a href="/wiki/Hera" title="Hera">Hera</a>, o dodecágono a <a href="/wiki/Zeus" title="Zeus">Zeus</a> e o polígono de 56 lados à criatura demoníaca <a href="/wiki/Tif%C3%A3o" title="Tifão">Tifão</a>.<sup id="cite_ref-plutarco.isis.osiris.30_9-0" class="reference"><a href="#cite_note-plutarco.isis.osiris.30-9"><span>[</span>9<span>]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Ver_também"><span id="Ver_tamb.C3.A9m"></span>Ver também</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pol%C3%ADgono&veaction=edit&section=21" title="Editar secção: Ver também" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Pol%C3%ADgono&action=edit&section=21" title="Editar código-fonte da secção: Ver também"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Poliedro" title="Poliedro">Poliedro</a></li></ul> <h2 id="Referências" style="cursor: help;" title="Esta seção foi configurada para não ser editável diretamente. Edite a página toda ou a seção anterior em vez disso."><span id="Refer.C3.AAncias"></span>Referências</h2> <div class="reflist" style="list-style-type: decimal;"><div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><cite class="citation web"><a rel="nofollow" class="external text" href="http://www.priberam.pt/dlpo/poligono">«Dicionário Priberam da Língua Portuguesa: polígono»</a>. Priberam Informática<span class="reference-accessdate">. Consultado em 3 de dezembro de 2014</span></cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fpt.wikipedia.org%3APol%C3gono&rft.btitle=Dicion%C3%A1rio+Priberam+da+L%C3ngua+Portuguesa%3A+pol%C3gono&rft.genre=unknown&rft.pub=Priberam+Inform%C3%A1tica&rft_id=http%3A%2F%2Fwww.priberam.pt%2Fdlpo%2Fpoligono&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-euclides.elementos.1.def.23-2"><span class="mw-cite-backlink"><a href="#cite_ref-euclides.elementos.1.def.23_2-0">↑</a></span> <span class="reference-text"><a href="/wiki/Euclides" title="Euclides">Euclides</a>, <i><a href="/wiki/Os_Elementos" title="Os Elementos">Os Elementos</a></i>, Livro I, <i>Definição 23</i> <a href="https://pt.wikisource.org/wiki/en:Page:The_Elements_of_Euclid_for_the_Use_of_Schools_and_Colleges_-_1872.djvu/27" class="extiw" title="s:en:Page:The Elements of Euclid for the Use of Schools and Colleges - 1872.djvu/27">[em linha]</a></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text"><cite class="citation web">Romirys Cavalcante. <a rel="nofollow" class="external text" href="https://www.vivendoentresimbolos.com/2013/11/o-que-e-uma-linha-poligonal.html">«O que é uma linha poligonal?»</a><span class="reference-accessdate">. Consultado em 26 de março de 2019</span></cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fpt.wikipedia.org%3APol%C3gono&rft.au=Romirys+Cavalcante&rft.btitle=O+que+%C3%A9+uma+linha+poligonal%3F&rft.genre=unknown&rft_id=https%3A%2F%2Fwww.vivendoentresimbolos.com%2F2013%2F11%2Fo-que-e-uma-linha-poligonal.html&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text"><cite class="citation book">Victor G. Ganzha, Evgenii V. Vorozhtsov. <i>Computer-Aided Analysis of Difference Schemes for Partial Differential Equations</i>. [S.l.]: John Wiley & Sons. <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Especial:Fontes_de_livros/978-1-118-03085-1" title="Especial:Fontes de livros/978-1-118-03085-1">978-1-118-03085-1</a></cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fpt.wikipedia.org%3APol%C3gono&rft.au=Victor+G.+Ganzha%2C+Evgenii+V.+Vorozhtsov&rft.btitle=Computer-Aided+Analysis+of+Difference+Schemes+for+Partial+Differential+Equations&rft.genre=book&rft.isbn=978-1-118-03085-1&rft.pub=John+Wiley+%26+Sons&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-:0-5"><span class="mw-cite-backlink">↑ <sup><i><b><a href="#cite_ref-:0_5-0">a</a></b></i></sup> <sup><i><b><a href="#cite_ref-:0_5-1">b</a></b></i></sup> <sup><i><b><a href="#cite_ref-:0_5-2">c</a></b></i></sup> <sup><i><b><a href="#cite_ref-:0_5-3">d</a></b></i></sup> <sup><i><b><a href="#cite_ref-:0_5-4">e</a></b></i></sup> <sup><i><b><a href="#cite_ref-:0_5-5">f</a></b></i></sup> <sup><i><b><a href="#cite_ref-:0_5-6">g</a></b></i></sup></span> <span class="reference-text"><cite class="citation book">Dolce, Osvaldo (2013). <i>Fundamentos de Matemática Elementar</i> 9 ed. [S.l.]: Atual. <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Especial:Fontes_de_livros/978-85-357-1686-3" title="Especial:Fontes de livros/978-85-357-1686-3">978-85-357-1686-3</a></cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fpt.wikipedia.org%3APol%C3gono&rft.aufirst=Osvaldo&rft.aulast=Dolce&rft.btitle=Fundamentos+de+Matem%C3%A1tica+Elementar&rft.date=2013&rft.edition=9&rft.genre=book&rft.isbn=978-85-357-1686-3&rft.pub=Atual&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><a href="#cite_ref-6">↑</a></span> <span class="reference-text"><span class="citation mathworld" id="Reference-Mathworld-Concave_Polygon"><cite id="CITEREFWeisstein" class="citation web">Terr, David; <a href="/wiki/Eric_W._Weisstein" title="Eric W. Weisstein">Weisstein, Eric W.</a> <a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/ConcavePolygon.html">«Concave Polygon»</a>. <i><a href="/wiki/MathWorld" title="MathWorld">MathWorld</a></i> (em inglês)<span class="reference-accessdate">. Consultado em 26 de março de 2019</span></cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fpt.wikipedia.org%3APol%C3gono&rft.atitle=Concave+Polygon&rft.au=Terr%2C+David&rft.au=Weisstein%2C+Eric+W.&rft.genre=unknown&rft.jtitle=MathWorld&rft_id=https%3A%2F%2Fmathworld.wolfram.com%2FConcavePolygon.html&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><a href="#cite_ref-7">↑</a></span> <span class="reference-text"><cite class="citation web">R. S. Schaeffer. <a rel="nofollow" class="external text" href="https://faculty.kutztown.edu/schaeffe/Tutorials/General/Polygons.html">«Naming Polygons»</a>. Kutztown University<span class="reference-accessdate">. Consultado em 26 de março de 2019</span></cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fpt.wikipedia.org%3APol%C3gono&rft.au=R.+S.+Schaeffer&rft.btitle=Naming+Polygons&rft.genre=unknown&rft.pub=Kutztown+University&rft_id=https%3A%2F%2Ffaculty.kutztown.edu%2Fschaeffe%2FTutorials%2FGeneral%2FPolygons.html&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><a href="#cite_ref-8">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external free" href="http://mathworld.wolfram.com/Myriagon.html">http://mathworld.wolfram.com/Myriagon.html</a></span> </li> <li id="cite_note-plutarco.isis.osiris.30-9"><span class="mw-cite-backlink"><a href="#cite_ref-plutarco.isis.osiris.30_9-0">↑</a></span> <span class="reference-text"><a href="/wiki/Eudoxo_de_Cnido" title="Eudoxo de Cnido">Eudoxo</a>, citado por <a href="/wiki/Plutarco" title="Plutarco">Plutarco</a>, <i>Moralia</i>, <i>Ísis e Osíris</i>, 30 <a rel="nofollow" class="external text" href="http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Plutarch/Moralia/Isis_and_Osiris*/B.html">[em linha]</a></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Ligações_externas"><span id="Liga.C3.A7.C3.B5es_externas"></span>Ligações externas</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pol%C3%ADgono&veaction=edit&section=22" title="Editar secção: Ligações externas" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Pol%C3%ADgono&action=edit&section=22" title="Editar código-fonte da secção: Ligações externas"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20100210185033/http://pessoal.sercomtel.com.br/matematica/fundam/geometria/geo-poli.htm">Geometria: Polígonos e triângulos</a></li></ul> <div role="navigation" class="navbox" aria-labelledby="Polígonos" style="padding:3px"><table class="nowraplinks collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div class="plainlinks hlist navbar mini"><ul><li class="nv-ver"><a href="/wiki/Predefini%C3%A7%C3%A3o:Pol%C3%ADgonos" title="Predefinição:Polígonos"><abbr title="Ver esta predefinição" style=";;background:none transparent;border:none;-moz-box-shadow:none;-webkit-box-shadow:none;box-shadow:none; padding:0;">v</abbr></a></li><li class="nv-discutir"><a href="/wiki/Predefini%C3%A7%C3%A3o_Discuss%C3%A3o:Pol%C3%ADgonos" title="Predefinição Discussão:Polígonos"><abbr title="Discutir esta predefinição" style=";;background:none transparent;border:none;-moz-box-shadow:none;-webkit-box-shadow:none;box-shadow:none; padding:0;">d</abbr></a></li><li class="nv-editar"><a class="external text" href="https://pt.wikipedia.org/w/index.php?title=Predefini%C3%A7%C3%A3o:Pol%C3%ADgonos&action=edit"><abbr title="Editar esta predefinição" style=";;background:none transparent;border:none;-moz-box-shadow:none;-webkit-box-shadow:none;box-shadow:none; padding:0;">e</abbr></a></li></ul></div><div id="Polígonos" style="font-size:114%;margin:0 4em"><a class="mw-selflink selflink">Polígonos</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Convexos</th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><style data-mw-deduplicate="TemplateStyles:r57040861">.mw-parser-output .sep-list{font-weight:bold}</style><span class="nowrap"><a href="/wiki/Tri%C3%A2ngulo" title="Triângulo">Triângulo</a></span> <span class="sep-list">·</span> <span class="nowrap"><a href="/wiki/Quadril%C3%A1tero" title="Quadrilátero">Quadrilátero</a></span> <span class="sep-list">·</span> <span class="nowrap"><a href="/wiki/Hept%C3%A1gono" title="Heptágono">Heptágono</a></span> <span class="sep-list">·</span> <span class="nowrap"><a href="/wiki/Oct%C3%B3gono" title="Octógono">Octógono</a></span> <span class="sep-list">·</span> <span class="nowrap"><a class="mw-selflink-fragment" href="#Quanto_ao_número_de_lados">Eneágono</a></span> <span class="sep-list">·</span> <span class="nowrap"><a href="/wiki/Heptadec%C3%A1gono" title="Heptadecágono">Heptadecágono</a></span> <span class="sep-list">·</span> <span class="nowrap"><a href="/wiki/Octodec%C3%A1gono" title="Octodecágono">Octodecágono</a></span> <span class="sep-list">·</span> <span class="nowrap"><a href="/wiki/Hendecos%C3%A1gono" title="Hendecoságono">Hendecoságono</a></span> <span class="sep-list">·</span> <span class="nowrap"><a href="/wiki/Docos%C3%A1gono" title="Docoságono">Docoságono</a></span> <span class="sep-list">·</span> <span class="nowrap"><a href="/wiki/Pentacos%C3%A1gono" title="Pentacoságono">Pentacoságono</a></span> <span class="sep-list">·</span> <span class="nowrap"><a href="/wiki/Triacont%C3%A1gono" title="Triacontágono">Triacontágono</a></span> <span class="sep-list">·</span> <span class="nowrap"><a href="/wiki/Tetracont%C3%A1gono" title="Tetracontágono">Tetracontágono</a></span> <span class="sep-list">·</span> <span class="nowrap"><a href="/wiki/Quili%C3%A1gono" title="Quiliágono">Quiliágono</a></span> <span class="sep-list">·</span> <span class="nowrap"><a href="/wiki/65537-gono" title="65537-gono">65537-gono</a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Estrela_(pol%C3%ADgono)" title="Estrela (polígono)">Estrelas</a></th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r57040861"><span class="nowrap"><a href="/wiki/Pentagrama" title="Pentagrama">Pentagrama</a></span> <span class="sep-list">·</span> <span class="nowrap"><a href="/wiki/Hexagrama" title="Hexagrama">Hexagrama</a></span> <span class="sep-list">·</span> <span class="nowrap"><a href="/wiki/Octograma" title="Octograma">Octograma</a></span></div></td></tr></tbody></table></div> <div role="navigation" class="navbox" aria-labelledby="Controle_de_autoridade" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th id="Controle_de_autoridade" scope="row" class="navbox-group" style="width:1%;width: 12%; text-align:center;"><a href="/wiki/Ajuda:Controle_de_autoridade" title="Ajuda:Controle de autoridade">Controle de autoridade</a></th><td class="navbox-list navbox-odd plainlinks" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><span style="white-space:nowrap;"><span typeof="mw:File"><a href="https://www.wikidata.org/wiki/Wikidata:Main_Page" title="Wikidata"><img alt="Wd" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/20px-Wikidata-logo.svg.png" decoding="async" width="20" height="11" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/30px-Wikidata-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/40px-Wikidata-logo.svg.png 2x" data-file-width="1050" data-file-height="590" /></a></span>: <span class="uid"><a href="https://www.wikidata.org/wiki/Q37555" class="extiw" title="wikidata:Q37555">Q37555</a></span></span></li> <li><span style="white-space:nowrap;"><a href="/wiki/Tesauro_de_Arte_e_Arquitetura" title="Tesauro de Arte e Arquitetura">AAT</a>: <span class="uid"><span class="plainlinks"><a rel="nofollow" class="external text" href="https://www.getty.edu/vow/AATFullDisplay?find=&logic=AND&note=&subjectid=300055633">300055633</a></span></span></span></li> <li><span style="white-space:nowrap;"><a href="/wiki/Biblioteca_Nacional_Central_de_Floren%C3%A7a" title="Biblioteca Nacional Central de Florença">BNCF</a>: <span class="uid"><span class="plainlinks"><a rel="nofollow" class="external text" href="https://thes.bncf.firenze.sbn.it/termine.php?id=6803">6803</a></span></span></span></li> <li><span style="white-space:nowrap;"><a href="/wiki/Biblioteca_Nacional_da_Fran%C3%A7a" title="Biblioteca Nacional da França">BNF</a>: <span class="uid"><span class="plainlinks"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb12266998h">12266998h</a></span></span></span></li> <li><span style="white-space:nowrap;"><a href="/wiki/Grande_Enciclop%C3%A9dia_Sovi%C3%A9tica" title="Grande Enciclopédia Soviética">BRE</a>: <span class="uid"><span class="plainlinks"><a rel="nofollow" class="external text" href="https://old.bigenc.ru/text/2220737">2220737</a></span></span></span></li> <li><span style="white-space:nowrap;"><a href="/wiki/Encyclop%C3%A6dia_Britannica" title="Encyclopædia Britannica">EBID</a>: <span class="uid"><span class="plainlinks"><a rel="nofollow" class="external text" href="https://www.britannica.com/topic/polygon-mathematics">ID</a></span></span></span></li> <li><span style="white-space:nowrap;"><a href="/wiki/Gemeinsame_Normdatei" title="Gemeinsame Normdatei">GND</a>: <span class="uid"><span class="plainlinks"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4175197-8">4175197-8</a></span></span></span></li> <li><span style="white-space:nowrap;"><a href="/wiki/JSTOR" title="JSTOR">JSTOR</a>: <span class="uid"><span class="plainlinks"><a rel="nofollow" class="external text" href="https://web.archive.org/web/*/https://www.jstor.org/topic/polygons">polygons</a></span></span></span></li> <li><span style="white-space:nowrap;"><a href="/wiki/N%C3%BAmero_de_controle_da_Biblioteca_do_Congresso" title="Número de controle da Biblioteca do Congresso">LCCN</a>: <span class="uid"><span class="plainlinks"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/sh85104637">sh85104637</a></span></span></span></li> <li><span style="white-space:nowrap;"><a href="/wiki/Enciclop%C3%A9dia_Treccani" title="Enciclopédia Treccani">Treccani</a>: <span class="uid"><span class="plainlinks"><a rel="nofollow" class="external text" href="https://www.treccani.it/enciclopedia/poligono">poligono</a></span></span></span></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Obtida de "<a dir="ltr" href="https://pt.wikipedia.org/w/index.php?title=Polígono&oldid=68484957">https://pt.wikipedia.org/w/index.php?title=Polígono&oldid=68484957</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Especial:Categorias" title="Especial:Categorias">Categoria</a>: <ul><li><a href="/wiki/Categoria:Pol%C3%ADgonos" title="Categoria:Polígonos">Polígonos</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Categorias ocultas: <ul><li><a href="/wiki/Categoria:!CS1_ingl%C3%AAs-fontes_em_l%C3%ADngua_(en)" title="Categoria:!CS1 inglês-fontes em língua (en)">!CS1 inglês-fontes em língua (en)</a></li><li><a href="/wiki/Categoria:!Artigos_que_carecem_de_notas_de_rodap%C3%A9_desde_outubro_de_2011" title="Categoria:!Artigos que carecem de notas de rodapé desde outubro de 2011">!Artigos que carecem de notas de rodapé desde outubro de 2011</a></li><li><a href="/wiki/Categoria:!Artigos_que_carecem_de_notas_de_rodap%C3%A9_sem_indica%C3%A7%C3%A3o_de_tema" title="Categoria:!Artigos que carecem de notas de rodapé sem indicação de tema">!Artigos que carecem de notas de rodapé sem indicação de tema</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Esta página foi editada pela última vez às 14h30min de 20 de agosto de 2024.</li> <li id="footer-info-copyright">Este texto é disponibilizado nos termos da licença <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.pt">Atribuição-CompartilhaIgual 4.0 Internacional (CC BY-SA 4.0) da Creative Commons</a>; 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