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rootpage-Área skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Saltar ao contido</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="Sitio"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="Menú principal" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-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-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">Menú principal</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">Menú principal</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">mover á barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">agochar</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navegación </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Portada" title="Visitar a páxina principal [z]" accesskey="z"><span>Portada</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedia:Portal_da_comunidade" title="Información acerca do proxecto, do que pode facer e dos lugares onde atopar as cousas"><span>Portal da comunidade</span></a></li><li id="n-A-Taberna" class="mw-list-item"><a href="/wiki/Wikipedia:A_Taberna"><span>A Taberna</span></a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/Wikipedia:Actualidade" title="Información acerca de acontecementos de actualidade"><span>Actualidade</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Especial:Cambios_recentes" title="A lista de modificacións recentes no wiki [r]" accesskey="r"><span>Cambios recentes</span></a></li><li id="n-Artigos-de-calidade" class="mw-list-item"><a href="/wiki/Wikipedia:Artigos_de_calidade"><span>Artigos de calidade</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Especial:Ao_chou" title="Cargar unha páxina ao chou [x]" accesskey="x"><span>Páxina ao chou</span></a></li><li id="n-help" class="mw-list-item"><a href="/wiki/Wikipedia:Axuda" title="O lugar para informarse"><span>Axuda</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Portada" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="a Wikipedia en galego" src="/static/images/mobile/copyright/wikipedia-tagline-gl.svg" width="118" height="13" style="width: 7.375em; height: 0.8125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Especial:Procurar" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Procurar neste wiki [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Procura</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Procurar en Wikipedia" aria-label="Procurar en Wikipedia" autocapitalize="sentences" title="Procurar neste wiki [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Especial:Procurar"> </div> <button class="cdx-button cdx-search-input__end-button">Procurar</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Ferramentas persoais"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Aparencia"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Cambia a aparencia do tamaño da fonte, o ancho e a cor da páxina" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Aparencia" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-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-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Aparencia</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_gl.wikipedia.org&uselang=gl" class=""><span>Doazóns</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Especial:Crear_unha_conta&returnto=%C3%81rea" title="É recomendable que cree unha conta e acceda ao sistema, se ben non é obrigatorio" class=""><span>Crear unha conta</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Especial:Iniciar_sesi%C3%B3n&returnto=%C3%81rea" title="É recomendable que se rexistre, se ben non é obrigatorio [o]" accesskey="o" class=""><span>Acceder ao sistema</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Máis opcións" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Ferramentas persoais" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-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-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Ferramentas persoais</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Menú de usuario" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_gl.wikipedia.org&uselang=gl"><span>Doazóns</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Especial:Crear_unha_conta&returnto=%C3%81rea" title="É recomendable que cree unha conta e acceda ao sistema, se ben non é obrigatorio"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Crear unha conta</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Especial:Iniciar_sesi%C3%B3n&returnto=%C3%81rea" title="É recomendable que se rexistre, se ben non é obrigatorio [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Acceder ao sistema</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Páxinas para os editores sen a sesión iniciada <a href="/wiki/Axuda:Introduci%C3%B3n" aria-label="Máis información sobre a edición"><span>máis información</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Especial:As_mi%C3%B1as_contribuci%C3%B3ns" title="Unha lista das modificacións feitas desde este enderezo IP [y]" accesskey="y"><span>Contribucións</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Especial:A_mi%C3%B1a_conversa" title="Conversa acerca de edicións feitas desde este enderezo IP [n]" accesskey="n"><span>Conversa</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Sitio"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Contidos" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Contidos</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">mover á barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">agochar</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Inicio</div> </a> </li> <li id="toc-Historia" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Historia"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Historia</span> </div> </a> <ul id="toc-Historia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Área_de_figuras_planas" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Área_de_figuras_planas"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Área de figuras planas</span> </div> </a> <button aria-controls="toc-Área_de_figuras_planas-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>Mostrar ou agochar a subsección "Área de figuras planas"</span> </button> <ul id="toc-Área_de_figuras_planas-sublist" class="vector-toc-list"> <li id="toc-Área_dun_triángulo" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Área_dun_triángulo"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Área dun triángulo</span> </div> </a> <ul id="toc-Área_dun_triángulo-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Área_dun_cuadrilátero" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Área_dun_cuadrilátero"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Área dun cuadrilátero</span> </div> </a> <ul id="toc-Área_dun_cuadrilátero-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Área_do_círculo_e_a_elipse" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Área_do_círculo_e_a_elipse"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Área do círculo e a elipse</span> </div> </a> <ul id="toc-Área_do_círculo_e_a_elipse-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Área_delimitada_entre_dúas_funcións" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Área_delimitada_entre_dúas_funcións"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Área delimitada entre dúas funcións</span> </div> </a> <ul id="toc-Área_delimitada_entre_dúas_funcións-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Área_de_superficies_curvas" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Área_de_superficies_curvas"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Área de superficies curvas</span> </div> </a> <button aria-controls="toc-Área_de_superficies_curvas-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>Mostrar ou agochar a subsección "Área de superficies curvas"</span> </button> <ul id="toc-Área_de_superficies_curvas-sublist" class="vector-toc-list"> <li id="toc-Superficie_de_revolución" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Superficie_de_revolución"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Superficie de revolución</span> </div> </a> <ul id="toc-Superficie_de_revolución-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cálculo_xeral_de_áreas" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Cálculo_xeral_de_áreas"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Cálculo xeral de áreas</span> </div> </a> <ul id="toc-Cálculo_xeral_de_áreas-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Unidades_de_medida_de_superficies" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Unidades_de_medida_de_superficies"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Unidades de medida de superficies</span> </div> </a> <button aria-controls="toc-Unidades_de_medida_de_superficies-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>Mostrar ou agochar a subsección "Unidades de medida de superficies"</span> </button> <ul id="toc-Unidades_de_medida_de_superficies-sublist" class="vector-toc-list"> <li id="toc-Sistema_métrico_(SI)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Sistema_métrico_(SI)"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Sistema métrico (SI)</span> </div> </a> <ul id="toc-Sistema_métrico_(SI)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sistema_inglés_de_medidas" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Sistema_inglés_de_medidas"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Sistema inglés de medidas</span> </div> </a> <ul id="toc-Sistema_inglés_de_medidas-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Notas" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notas"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Notas</span> </div> </a> <ul id="toc-Notas-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Véxase_tamén" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Véxase_tamén"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Véxase tamén</span> </div> </a> <button aria-controls="toc-Véxase_tamén-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>Mostrar ou agochar a subsección "Véxase tamén"</span> </button> <ul id="toc-Véxase_tamén-sublist" class="vector-toc-list"> <li id="toc-Bibliografía" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bibliografía"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Bibliografía</span> </div> </a> <ul id="toc-Bibliografía-sublist" class="vector-toc-list"> </ul> </li> </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="Contidos" 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="Mostrar ou agochar a táboa de contidos" > <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">Mostrar ou agochar a táboa de contidos</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">Área</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 a un artigo noutra lingua. Dispoñible en 164 linguas" > <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-164" 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">164 linguas</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Oppervlakte" title="Oppervlakte – afrikaans" lang="af" hreflang="af" data-title="Oppervlakte" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Fl%C3%A4cheninhalt" title="Flächeninhalt – alemán suízo" lang="gsw" hreflang="gsw" data-title="Flächeninhalt" data-language-autonym="Alemannisch" data-language-local-name="alemán suízo" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Aria" title="Aria – aragonés" lang="an" hreflang="an" data-title="Aria" data-language-autonym="Aragonés" data-language-local-name="aragonés" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-anp mw-list-item"><a href="https://anp.wikipedia.org/wiki/%E0%A4%95%E0%A5%8D%E0%A4%B7%E0%A5%87%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%AB%E0%A4%B2" title="क्षेत्रफल – angika" lang="anp" hreflang="anp" data-title="क्षेत्रफल" data-language-autonym="अंगिका" data-language-local-name="angika" class="interlanguage-link-target"><span>अंगिका</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%B3%D8%A7%D8%AD%D8%A9" title="مساحة – árabe" lang="ar" hreflang="ar" data-title="مساحة" data-language-autonym="العربية" data-language-local-name="árabe" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-arc mw-list-item"><a href="https://arc.wikipedia.org/wiki/%DC%AB%DC%9B%DC%9D%DC%9A%DC%98%DC%AC%DC%90" title="ܫܛܝܚܘܬܐ – arameo" lang="arc" hreflang="arc" data-title="ܫܛܝܚܘܬܐ" data-language-autonym="ܐܪܡܝܐ" data-language-local-name="arameo" class="interlanguage-link-target"><span>ܐܪܡܝܐ</span></a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D8%AA%D9%8A%D8%B3%D8%A7%D8%B9" title="تيساع – Moroccan Arabic" lang="ary" hreflang="ary" data-title="تيساع" data-language-autonym="الدارجة" data-language-local-name="Moroccan Arabic" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D9%85%D8%B3%D8%A7%D8%AD%D9%87" title="مساحه – Egyptian Arabic" lang="arz" hreflang="arz" data-title="مساحه" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%95%E0%A7%8D%E0%A6%B7%E0%A7%87%E0%A6%A4%E0%A7%8D%E0%A7%B0%E0%A6%AB%E0%A6%B2" title="ক্ষেত্ৰফল – assamés" lang="as" hreflang="as" data-title="ক্ষেত্ৰফল" data-language-autonym="অসমীয়া" data-language-local-name="assamés" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/%C3%81rea_(xeometr%C3%ADa)" title="Área (xeometría) – asturiano" lang="ast" hreflang="ast" data-title="Área (xeometría)" data-language-autonym="Asturianu" data-language-local-name="asturiano" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-av mw-list-item"><a href="https://av.wikipedia.org/wiki/%D0%9F%D0%BB%D0%BE%D1%89%D0%B0%D0%B4%D1%8C" title="Площадь – avar" lang="av" hreflang="av" data-title="Площадь" data-language-autonym="Авар" data-language-local-name="avar" class="interlanguage-link-target"><span>Авар</span></a></li><li class="interlanguage-link interwiki-awa mw-list-item"><a href="https://awa.wikipedia.org/wiki/%E0%A4%95%E0%A5%8D%E0%A4%B7%E0%A5%87%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%AB%E0%A4%B2" title="क्षेत्रफल – awadhi" lang="awa" hreflang="awa" data-title="क्षेत्रफल" data-language-autonym="अवधी" data-language-local-name="awadhi" class="interlanguage-link-target"><span>अवधी</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Sah%C9%99_(%C3%B6l%C3%A7%C3%BC_parametri)" title="Sahə (ölçü parametri) – acerbaixano" lang="az" hreflang="az" data-title="Sahə (ölçü parametri)" data-language-autonym="Azərbaycanca" data-language-local-name="acerbaixano" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D9%85%D8%B3%D8%A7%D8%AD%D8%AA" title="مساحت – South Azerbaijani" lang="azb" hreflang="azb" data-title="مساحت" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%9C%D0%B0%D0%B9%D2%99%D0%B0%D0%BD" title="Майҙан – baxkir" lang="ba" hreflang="ba" data-title="Майҙан" data-language-autonym="Башҡортса" data-language-local-name="baxkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Fl%C3%A4chn" title="Flächn – Bavarian" lang="bar" hreflang="bar" data-title="Flächn" data-language-autonym="Boarisch" data-language-local-name="Bavarian" class="interlanguage-link-target"><span>Boarisch</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Pluots" title="Pluots – Samogitian" lang="sgs" hreflang="sgs" data-title="Pluots" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Hiwas" title="Hiwas – Central Bikol" lang="bcl" hreflang="bcl" data-title="Hiwas" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9F%D0%BB%D0%BE%D1%88%D1%87%D0%B0" title="Плошча – belaruso" lang="be" hreflang="be" data-title="Плошча" data-language-autonym="Беларуская" data-language-local-name="belaruso" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9F%D0%BB%D0%BE%D1%88%D1%87%D0%B0" title="Плошча – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Плошча" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9F%D0%BB%D0%BE%D1%89" title="Площ – búlgaro" lang="bg" hreflang="bg" data-title="Площ" data-language-autonym="Български" data-language-local-name="búlgaro" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%95%E0%A5%8D%E0%A4%B7%E0%A5%87%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%AB%E0%A4%B2" title="क्षेत्रफल – Bhojpuri" lang="bh" hreflang="bh" data-title="क्षेत्रफल" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target"><span>भोजपुरी</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%95%E0%A7%8D%E0%A6%B7%E0%A7%87%E0%A6%A4%E0%A7%8D%E0%A6%B0%E0%A6%AB%E0%A6%B2" title="ক্ষেত্রফল – bengalí" lang="bn" hreflang="bn" data-title="ক্ষেত্রফল" data-language-autonym="বাংলা" data-language-local-name="bengalí" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Gorread" title="Gorread – bretón" lang="br" hreflang="br" data-title="Gorread" data-language-autonym="Brezhoneg" data-language-local-name="bretón" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Povr%C5%A1ina" title="Površina – bosníaco" lang="bs" hreflang="bs" data-title="Površina" data-language-autonym="Bosanski" data-language-local-name="bosníaco" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-btm mw-list-item"><a href="https://btm.wikipedia.org/wiki/Bolak" title="Bolak – Batak Mandailing" lang="btm" hreflang="btm" data-title="Bolak" data-language-autonym="Batak Mandailing" data-language-local-name="Batak Mandailing" class="interlanguage-link-target"><span>Batak Mandailing</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/%C3%80rea" title="Àrea – catalán" lang="ca" hreflang="ca" data-title="Àrea" data-language-autonym="Català" data-language-local-name="catalán" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cdo mw-list-item"><a href="https://cdo.wikipedia.org/wiki/Mi%C3%AAng-c%C3%A9k" title="Miêng-cék – Mindong" lang="cdo" hreflang="cdo" data-title="Miêng-cék" data-language-autonym="閩東語 / Mìng-dĕ̤ng-ngṳ̄" data-language-local-name="Mindong" class="interlanguage-link-target"><span>閩東語 / Mìng-dĕ̤ng-ngṳ̄</span></a></li><li class="interlanguage-link interwiki-ce mw-list-item"><a href="https://ce.wikipedia.org/wiki/%D0%9C%D0%B0%D0%B9%D0%B4%D0%B0" title="Майда – checheno" lang="ce" hreflang="ce" data-title="Майда" data-language-autonym="Нохчийн" data-language-local-name="checheno" class="interlanguage-link-target"><span>Нохчийн</span></a></li><li class="interlanguage-link interwiki-ceb mw-list-item"><a href="https://ceb.wikipedia.org/wiki/Langyab" title="Langyab – cebuano" lang="ceb" hreflang="ceb" data-title="Langyab" data-language-autonym="Cebuano" data-language-local-name="cebuano" class="interlanguage-link-target"><span>Cebuano</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DA%95%D9%88%D9%88%D8%A8%DB%95%D8%B1" title="ڕووبەر – kurdo central" lang="ckb" hreflang="ckb" data-title="ڕووبەر" data-language-autonym="کوردی" data-language-local-name="kurdo 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/Obsah" title="Obsah – checo" lang="cs" hreflang="cs" data-title="Obsah" data-language-autonym="Čeština" data-language-local-name="checo" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cu mw-list-item"><a href="https://cu.wikipedia.org/wiki/%D0%9F%D1%80%D0%BE%D1%81%D1%82%D1%80%D0%B0%D0%BD%D0%B8%D1%A5" title="Пространиѥ – eslavo eclesiástico" lang="cu" hreflang="cu" data-title="Пространиѥ" data-language-autonym="Словѣньскъ / ⰔⰎⰑⰂⰡⰐⰠⰔⰍⰟ" data-language-local-name="eslavo eclesiástico" class="interlanguage-link-target"><span>Словѣньскъ / ⰔⰎⰑⰂⰡⰐⰠⰔⰍⰟ</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9B%D0%B0%D0%BF%D1%82%C4%83%D0%BA" title="Лаптăк – chuvaxo" lang="cv" hreflang="cv" data-title="Лаптăк" data-language-autonym="Чӑвашла" data-language-local-name="chuvaxo" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Arwynebedd" title="Arwynebedd – galés" lang="cy" hreflang="cy" data-title="Arwynebedd" data-language-autonym="Cymraeg" data-language-local-name="galés" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Areal" title="Areal – dinamarqués" lang="da" hreflang="da" data-title="Areal" data-language-autonym="Dansk" data-language-local-name="dinamarqués" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Fl%C3%A4cheninhalt" title="Flächeninhalt – alemán" lang="de" hreflang="de" data-title="Flächeninhalt" data-language-autonym="Deutsch" data-language-local-name="alemán" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-diq mw-list-item"><a href="https://diq.wikipedia.org/wiki/Erd" title="Erd – Zazaki" lang="diq" hreflang="diq" data-title="Erd" data-language-autonym="Zazaki" data-language-local-name="Zazaki" class="interlanguage-link-target"><span>Zazaki</span></a></li><li class="interlanguage-link interwiki-dsb mw-list-item"><a href="https://dsb.wikipedia.org/wiki/Wop%C5%9Bimje%C5%9Be_p%C5%82oni" title="Wopśimjeśe płoni – baixo sorbio" lang="dsb" hreflang="dsb" data-title="Wopśimjeśe płoni" data-language-autonym="Dolnoserbski" data-language-local-name="baixo sorbio" class="interlanguage-link-target"><span>Dolnoserbski</span></a></li><li class="interlanguage-link interwiki-dv mw-list-item"><a href="https://dv.wikipedia.org/wiki/%DE%87%DE%A6%DE%86%DE%A6%DE%89%DE%A8%DE%82%DE%B0" title="އަކަމިން – divehi" lang="dv" hreflang="dv" data-title="އަކަމިން" data-language-autonym="ދިވެހިބަސް" data-language-local-name="divehi" class="interlanguage-link-target"><span>ދިވެހިބަސް</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD" title="Εμβαδόν – grego" lang="el" hreflang="el" data-title="Εμβαδόν" 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/Area" title="Area – inglés" lang="en" hreflang="en" data-title="Area" data-language-autonym="English" data-language-local-name="inglés" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Areo" title="Areo – esperanto" lang="eo" hreflang="eo" data-title="Areo" 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/%C3%81rea" title="Área – español" lang="es" hreflang="es" data-title="Área" data-language-autonym="Español" data-language-local-name="español" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Pindala" title="Pindala – estoniano" lang="et" hreflang="et" data-title="Pindala" data-language-autonym="Eesti" data-language-local-name="estoniano" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Azalera" title="Azalera – éuscaro" lang="eu" hreflang="eu" data-title="Azalera" data-language-autonym="Euskara" data-language-local-name="éuscaro" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D8%B3%D8%A7%D8%AD%D8%AA" title="مساحت – persa" lang="fa" hreflang="fa" data-title="مساحت" data-language-autonym="فارسی" data-language-local-name="persa" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Pinta-ala" title="Pinta-ala – finés" lang="fi" hreflang="fi" data-title="Pinta-ala" data-language-autonym="Suomi" data-language-local-name="finés" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Pindala" title="Pindala – Võro" lang="vro" hreflang="vro" data-title="Pindala" data-language-autonym="Võro" data-language-local-name="Võro" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-fj mw-list-item"><a href="https://fj.wikipedia.org/wiki/Iwasewase" title="Iwasewase – fixiano" lang="fj" hreflang="fj" data-title="Iwasewase" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="fixiano" class="interlanguage-link-target"><span>Na Vosa Vakaviti</span></a></li><li class="interlanguage-link interwiki-fo mw-list-item"><a href="https://fo.wikipedia.org/wiki/V%C3%ADdd" title="Vídd – feroés" lang="fo" hreflang="fo" data-title="Vídd" data-language-autonym="Føroyskt" data-language-local-name="feroés" class="interlanguage-link-target"><span>Føroyskt</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Aire_(g%C3%A9om%C3%A9trie)" title="Aire (géométrie) – francés" lang="fr" hreflang="fr" data-title="Aire (géométrie)" data-language-autonym="Français" data-language-local-name="francés" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Areaal_(Miat)" title="Areaal (Miat) – frisón setentrional" lang="frr" hreflang="frr" data-title="Areaal (Miat)" data-language-autonym="Nordfriisk" data-language-local-name="frisón setentrional" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-fy mw-list-item"><a href="https://fy.wikipedia.org/wiki/Oerflak" title="Oerflak – frisón occidental" lang="fy" hreflang="fy" data-title="Oerflak" data-language-autonym="Frysk" data-language-local-name="frisón occidental" class="interlanguage-link-target"><span>Frysk</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E9%9D%A2%E7%A9%8D" title="面積 – Gan" lang="gan" hreflang="gan" data-title="面積" data-language-autonym="贛語" data-language-local-name="Gan" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/Farsaingeachd" title="Farsaingeachd – gaélico escocés" lang="gd" hreflang="gd" data-title="Farsaingeachd" data-language-autonym="Gàidhlig" data-language-local-name="gaélico escocés" class="interlanguage-link-target"><span>Gàidhlig</span></a></li><li class="interlanguage-link interwiki-gn mw-list-item"><a href="https://gn.wikipedia.org/wiki/Tendaha" title="Tendaha – guaraní" lang="gn" hreflang="gn" data-title="Tendaha" data-language-autonym="Avañe'ẽ" data-language-local-name="guaraní" class="interlanguage-link-target"><span>Avañe'ẽ</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%95%E0%AB%8D%E0%AA%B7%E0%AB%87%E0%AA%A4%E0%AB%8D%E0%AA%B0%E0%AA%AB%E0%AA%B3" title="ક્ષેત્રફળ – guxarati" lang="gu" hreflang="gu" data-title="ક્ષેત્રફળ" data-language-autonym="ગુજરાતી" data-language-local-name="guxarati" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-gv mw-list-item"><a href="https://gv.wikipedia.org/wiki/Eaghtyr" title="Eaghtyr – manx" lang="gv" hreflang="gv" data-title="Eaghtyr" 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/Mien-chit" title="Mien-chit – Hakka Chinese" lang="hak" hreflang="hak" data-title="Mien-chit" data-language-autonym="客家語 / Hak-kâ-ngî" data-language-local-name="Hakka Chinese" class="interlanguage-link-target"><span>客家語 / Hak-kâ-ngî</span></a></li><li class="interlanguage-link interwiki-haw mw-list-item"><a href="https://haw.wikipedia.org/wiki/%CA%BBAlea" title="ʻAlea – hawaiano" lang="haw" hreflang="haw" data-title="ʻAlea" data-language-autonym="Hawaiʻi" data-language-local-name="hawaiano" class="interlanguage-link-target"><span>Hawaiʻi</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A9%D7%98%D7%97" title="שטח – hebreo" lang="he" hreflang="he" data-title="שטח" data-language-autonym="עברית" data-language-local-name="hebreo" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%95%E0%A5%8D%E0%A4%B7%E0%A5%87%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%AB%E0%A4%B2" title="क्षेत्रफल – hindi" lang="hi" hreflang="hi" data-title="क्षेत्रफल" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Area" title="Area – Fiji Hindi" lang="hif" hreflang="hif" data-title="Area" data-language-autonym="Fiji Hindi" data-language-local-name="Fiji Hindi" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Povr%C5%A1ina" title="Površina – croata" lang="hr" hreflang="hr" data-title="Površina" data-language-autonym="Hrvatski" data-language-local-name="croata" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hsb mw-list-item"><a href="https://hsb.wikipedia.org/wiki/Wobsah_p%C5%99estrjenje" title="Wobsah přestrjenje – alto sorbio" lang="hsb" hreflang="hsb" data-title="Wobsah přestrjenje" data-language-autonym="Hornjoserbsce" data-language-local-name="alto sorbio" class="interlanguage-link-target"><span>Hornjoserbsce</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Ter%C3%BClet_(matematika)" title="Terület (matematika) – húngaro" lang="hu" hreflang="hu" data-title="Terület (matematika)" 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/%D5%84%D5%A1%D5%AF%D5%A5%D6%80%D5%A5%D5%BD" title="Մակերես – armenio" lang="hy" hreflang="hy" data-title="Մակերես" data-language-autonym="Հայերեն" data-language-local-name="armenio" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Area" title="Area – interlingua" lang="ia" hreflang="ia" data-title="Area" data-language-autonym="Interlingua" data-language-local-name="interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Luas" title="Luas – indonesio" lang="id" hreflang="id" data-title="Luas" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesio" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ilo mw-list-item"><a href="https://ilo.wikipedia.org/wiki/Kalawa" title="Kalawa – ilocano" lang="ilo" hreflang="ilo" data-title="Kalawa" data-language-autonym="Ilokano" data-language-local-name="ilocano" class="interlanguage-link-target"><span>Ilokano</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Areo" title="Areo – ido" lang="io" hreflang="io" data-title="Areo" data-language-autonym="Ido" data-language-local-name="ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Flatarm%C3%A1l" title="Flatarmál – islandés" lang="is" hreflang="is" data-title="Flatarmál" data-language-autonym="Íslenska" data-language-local-name="islandés" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Area" title="Area – italiano" lang="it" hreflang="it" data-title="Area" 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/%E9%9D%A2%E7%A9%8D" title="面積 – xaponés" lang="ja" hreflang="ja" data-title="面積" data-language-autonym="日本語" data-language-local-name="xaponés" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Ieria" title="Ieria – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Ieria" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Jembar" title="Jembar – xavanés" lang="jv" hreflang="jv" data-title="Jembar" data-language-autonym="Jawa" data-language-local-name="xavanés" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A4%E1%83%90%E1%83%A0%E1%83%97%E1%83%9D%E1%83%91%E1%83%98" title="ფართობი – xeorxiano" lang="ka" hreflang="ka" data-title="ფართობი" data-language-autonym="ქართული" data-language-local-name="xeorxiano" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Tajumma" title="Tajumma – cabila" lang="kab" hreflang="kab" data-title="Tajumma" data-language-autonym="Taqbaylit" data-language-local-name="cabila" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-kbd mw-list-item"><a href="https://kbd.wikipedia.org/wiki/%D0%A9%D3%80%D1%8B%D0%BF%D3%80%D1%8D_%D0%B8%D0%BD%D0%B0%D0%B3%D1%8A" title="ЩӀыпӀэ инагъ – cabardiano" lang="kbd" hreflang="kbd" data-title="ЩӀыпӀэ инагъ" 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%90%D1%83%D0%B4%D0%B0%D0%BD_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F)" title="Аудан (геометрия) – kazako" lang="kk" hreflang="kk" data-title="Аудан (геометрия)" data-language-autonym="Қазақша" data-language-local-name="kazako" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%80%E1%9F%92%E1%9E%9A%E1%9E%9B%E1%9E%B6%E1%9E%95%E1%9F%92%E1%9E%91%E1%9F%83" title="ក្រលាផ្ទៃ – khmer" lang="km" hreflang="km" data-title="ក្រលាផ្ទៃ" 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%84%93%EC%9D%B4" title="넓이 – coreano" lang="ko" hreflang="ko" data-title="넓이" 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/R%C3%BBerd" title="Rûerd – kurdo" lang="ku" hreflang="ku" data-title="Rûerd" data-language-autonym="Kurdî" data-language-local-name="kurdo" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-kw mw-list-item"><a href="https://kw.wikipedia.org/wiki/Enep_(fysegieth)" title="Enep (fysegieth) – córnico" lang="kw" hreflang="kw" data-title="Enep (fysegieth)" data-language-autonym="Kernowek" data-language-local-name="córnico" class="interlanguage-link-target"><span>Kernowek</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%90%D1%8F%D0%BD%D1%82" title="Аянт – kirguiz" lang="ky" hreflang="ky" data-title="Аянт" data-language-autonym="Кыргызча" data-language-local-name="kirguiz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Area_(geometria)" title="Area (geometria) – latín" lang="la" hreflang="la" data-title="Area (geometria)" data-language-autonym="Latina" data-language-local-name="latín" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Fl%C3%A4ch" title="Fläch – luxemburgués" lang="lb" hreflang="lb" data-title="Fläch" data-language-autonym="Lëtzebuergesch" data-language-local-name="luxemburgués" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Oppervlak" title="Oppervlak – limburgués" lang="li" hreflang="li" data-title="Oppervlak" data-language-autonym="Limburgs" data-language-local-name="limburgués" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-lij mw-list-item"><a href="https://lij.wikipedia.org/wiki/Area" title="Area – Ligurian" lang="lij" hreflang="lij" data-title="Area" data-language-autonym="Ligure" data-language-local-name="Ligurian" class="interlanguage-link-target"><span>Ligure</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Area" title="Area – Lombard" lang="lmo" hreflang="lmo" data-title="Area" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-ln mw-list-item"><a href="https://ln.wikipedia.org/wiki/Etando" title="Etando – lingala" lang="ln" hreflang="ln" data-title="Etando" data-language-autonym="Lingála" data-language-local-name="lingala" class="interlanguage-link-target"><span>Lingála</span></a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%E0%BB%80%E0%BA%99%E0%BA%B7%E0%BB%89%E0%BA%AD%E0%BA%97%E0%BA%B5%E0%BB%88" title="ເນື້ອທີ່ – laosiano" lang="lo" hreflang="lo" data-title="ເນື້ອທີ່" data-language-autonym="ລາວ" data-language-local-name="laosiano" class="interlanguage-link-target"><span>ລາວ</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Plotas" title="Plotas – lituano" lang="lt" hreflang="lt" data-title="Plotas" 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/Laukums" title="Laukums – letón" lang="lv" hreflang="lv" data-title="Laukums" data-language-autonym="Latviešu" data-language-local-name="letón" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mai mw-list-item"><a href="https://mai.wikipedia.org/wiki/%E0%A4%95%E0%A5%8D%E0%A4%B7%E0%A5%87%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%AB%E0%A4%B2" title="क्षेत्रफल – maithili" lang="mai" hreflang="mai" data-title="क्षेत्रफल" data-language-autonym="मैथिली" data-language-local-name="maithili" class="interlanguage-link-target"><span>मैथिली</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Velarantany" title="Velarantany – malgaxe" lang="mg" hreflang="mg" data-title="Velarantany" 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%9A%D1%83%D0%BC%D0%B4%D1%8B%D0%BA" title="Кумдык – Eastern Mari" lang="mhr" hreflang="mhr" data-title="Кумдык" data-language-autonym="Олык марий" data-language-local-name="Eastern Mari" class="interlanguage-link-target"><span>Олык марий</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9F%D0%BB%D0%BE%D1%88%D1%82%D0%B8%D0%BD%D0%B0" title="Плоштина – macedonio" lang="mk" hreflang="mk" data-title="Плоштина" data-language-autonym="Македонски" data-language-local-name="macedonio" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B5%E0%B4%BF%E0%B4%B8%E0%B5%8D%E0%B4%A4%E0%B5%80%E0%B5%BC%E0%B4%A3%E0%B5%8D%E0%B4%A3%E0%B4%82" title="വിസ്തീർണ്ണം – malabar" lang="ml" hreflang="ml" data-title="വിസ്തീർണ്ണം" data-language-autonym="മലയാളം" data-language-local-name="malabar" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A2%D0%B0%D0%BB%D0%B1%D0%B0%D0%B9" title="Талбай – mongol" lang="mn" hreflang="mn" data-title="Талбай" data-language-autonym="Монгол" data-language-local-name="mongol" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-mni mw-list-item"><a href="https://mni.wikipedia.org/wiki/%EA%AF%84%EA%AF%A5%EA%AF%9B%EA%AF%86%EA%AF%A5%EA%AF%8E%EA%AF%95" title="ꯄꯥꯛꯆꯥꯎꯕ – manipuri" lang="mni" hreflang="mni" data-title="ꯄꯥꯛꯆꯥꯎꯕ" data-language-autonym="ꯃꯤꯇꯩ ꯂꯣꯟ" data-language-local-name="manipuri" class="interlanguage-link-target"><span>ꯃꯤꯇꯩ ꯂꯣꯟ</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%95%E0%A5%8D%E0%A4%B7%E0%A5%87%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%AB%E0%A4%B3" title="क्षेत्रफळ – marathi" lang="mr" hreflang="mr" data-title="क्षेत्रफळ" data-language-autonym="मराठी" data-language-local-name="marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Luas" title="Luas – malaio" lang="ms" hreflang="ms" data-title="Luas" 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-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/%C3%81ria" title="Ária – mirandés" lang="mwl" hreflang="mwl" data-title="Ária" data-language-autonym="Mirandés" data-language-local-name="mirandés" class="interlanguage-link-target"><span>Mirandés</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%A7%E1%80%9B%E1%80%AD%E1%80%9A%E1%80%AC" title="ဧရိယာ – birmano" lang="my" hreflang="my" data-title="ဧရိယာ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="birmano" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-mzn mw-list-item"><a href="https://mzn.wikipedia.org/wiki/%DA%AF%D8%AA%DB%8C" title="گتی – mazandaraní" lang="mzn" hreflang="mzn" data-title="گتی" data-language-autonym="مازِرونی" data-language-local-name="mazandaraní" class="interlanguage-link-target"><span>مازِرونی</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Flach" title="Flach – baixo alemán" lang="nds" hreflang="nds" data-title="Flach" data-language-autonym="Plattdüütsch" data-language-local-name="baixo alemán" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-nds-nl mw-list-item"><a href="https://nds-nl.wikipedia.org/wiki/Oppervlakte" title="Oppervlakte – baixo saxón" lang="nds-NL" hreflang="nds-NL" data-title="Oppervlakte" data-language-autonym="Nedersaksies" data-language-local-name="baixo saxón" class="interlanguage-link-target"><span>Nedersaksies</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%95%E0%A5%8D%E0%A4%B7%E0%A5%87%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%AB%E0%A4%B2" title="क्षेत्रफल – nepalí" lang="ne" hreflang="ne" data-title="क्षेत्रफल" data-language-autonym="नेपाली" data-language-local-name="nepalí" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Oppervlakte" title="Oppervlakte – neerlandés" lang="nl" hreflang="nl" data-title="Oppervlakte" data-language-autonym="Nederlands" data-language-local-name="neerlandés" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Flatevidd" title="Flatevidd – noruegués nynorsk" lang="nn" hreflang="nn" data-title="Flatevidd" data-language-autonym="Norsk nynorsk" data-language-local-name="noruegués 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/Areal" title="Areal – noruegués bokmål" lang="nb" hreflang="nb" data-title="Areal" data-language-autonym="Norsk bokmål" data-language-local-name="noruegués 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/Aira" title="Aira – occitano" lang="oc" hreflang="oc" data-title="Aira" data-language-autonym="Occitan" data-language-local-name="occitano" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-os mw-list-item"><a href="https://os.wikipedia.org/wiki/%D0%A4%C3%A6%D0%B7%D1%83%D0%B0%D1%82" title="Фæзуат – ossetio" lang="os" hreflang="os" data-title="Фæзуат" data-language-autonym="Ирон" data-language-local-name="ossetio" class="interlanguage-link-target"><span>Ирон</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%96%E0%A9%87%E0%A8%A4%E0%A8%B0%E0%A8%AB%E0%A8%B2" title="ਖੇਤਰਫਲ – panxabí" lang="pa" hreflang="pa" data-title="ਖੇਤਰਫਲ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="panxabí" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pfl mw-list-item"><a href="https://pfl.wikipedia.org/wiki/Fl%C3%A4che" title="Fläche – Palatine German" lang="pfl" hreflang="pfl" data-title="Fläche" data-language-autonym="Pälzisch" data-language-local-name="Palatine German" class="interlanguage-link-target"><span>Pälzisch</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Pole_powierzchni" title="Pole powierzchni – polaco" lang="pl" hreflang="pl" data-title="Pole powierzchni" data-language-autonym="Polski" data-language-local-name="polaco" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%B1%D9%82%D8%A8%DB%81" title="رقبہ – Western Punjabi" lang="pnb" hreflang="pnb" data-title="رقبہ" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/%C3%81rea" title="Área – portugués" lang="pt" hreflang="pt" data-title="Área" data-language-autonym="Português" data-language-local-name="portugués" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Hallka_k%27iti_k%27anchar" title="Hallka k'iti k'anchar – quechua" lang="qu" hreflang="qu" data-title="Hallka k'iti k'anchar" data-language-autonym="Runa Simi" data-language-local-name="quechua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Arie" title="Arie – romanés" lang="ro" hreflang="ro" data-title="Arie" data-language-autonym="Română" data-language-local-name="romanés" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9F%D0%BB%D0%BE%D1%89%D0%B0%D0%B4%D1%8C" title="Площадь – ruso" lang="ru" hreflang="ru" data-title="Площадь" data-language-autonym="Русский" data-language-local-name="ruso" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sa mw-list-item"><a href="https://sa.wikipedia.org/wiki/%E0%A4%95%E0%A5%8D%E0%A4%B7%E0%A5%87%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%AB%E0%A4%B2%E0%A4%AE%E0%A5%8D" title="क्षेत्रफलम् – sánscrito" lang="sa" hreflang="sa" data-title="क्षेत्रफलम्" data-language-autonym="संस्कृतम्" data-language-local-name="sánscrito" class="interlanguage-link-target"><span>संस्कृतम्</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%98%D1%8D%D0%BD" title="Иэн – iacuto" lang="sah" hreflang="sah" data-title="Иэн" data-language-autonym="Саха тыла" data-language-local-name="iacuto" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/%C3%80ria_(supirfici)" title="Ària (supirfici) – siciliano" lang="scn" hreflang="scn" data-title="Ària (supirfici)" data-language-autonym="Sicilianu" data-language-local-name="siciliano" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Area" title="Area – escocés" lang="sco" hreflang="sco" data-title="Area" data-language-autonym="Scots" data-language-local-name="escocés" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D8%A7%D9%8A%D8%B1%D8%A7%D8%B6%D9%8A" title="ايراضي – sindhi" lang="sd" hreflang="sd" data-title="ايراضي" data-language-autonym="سنڌي" data-language-local-name="sindhi" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Povr%C5%A1ina" title="Površina – serbocroata" lang="sh" hreflang="sh" data-title="Površina" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbocroata" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Area" title="Area – Simple English" lang="en-simple" hreflang="en-simple" data-title="Area" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Plocha_(%C3%BAtvar)" title="Plocha (útvar) – eslovaco" lang="sk" hreflang="sk" data-title="Plocha (útvar)" 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/Povr%C5%A1ina" title="Površina – esloveno" lang="sl" hreflang="sl" data-title="Površina" 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/Nharaunda" title="Nharaunda – shona" lang="sn" hreflang="sn" data-title="Nharaunda" data-language-autonym="ChiShona" data-language-local-name="shona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Bed" title="Bed – somalí" lang="so" hreflang="so" data-title="Bed" data-language-autonym="Soomaaliga" data-language-local-name="somalí" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Sip%C3%ABrfaqja" title="Sipërfaqja – albanés" lang="sq" hreflang="sq" data-title="Sipërfaqja" data-language-autonym="Shqip" data-language-local-name="albanés" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9F%D0%BE%D0%B2%D1%80%D1%88%D0%B8%D0%BD%D0%B0" title="Површина – serbio" lang="sr" hreflang="sr" data-title="Површина" data-language-autonym="Српски / srpski" data-language-local-name="serbio" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Ar%C3%A9a" title="Aréa – sundanés" lang="su" hreflang="su" data-title="Aréa" data-language-autonym="Sunda" data-language-local-name="sundanés" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Area" title="Area – sueco" lang="sv" hreflang="sv" data-title="Area" 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/Eneo" title="Eneo – suahili" lang="sw" hreflang="sw" data-title="Eneo" data-language-autonym="Kiswahili" data-language-local-name="suahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-szl mw-list-item"><a href="https://szl.wikipedia.org/wiki/Plac_rozlygowa%C5%84o" title="Plac rozlygowańo – Silesian" lang="szl" hreflang="szl" data-title="Plac rozlygowańo" 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%B0%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AE%B3%E0%AE%B5%E0%AF%81" title="பரப்பளவு – támil" lang="ta" hreflang="ta" data-title="பரப்பளவு" data-language-autonym="தமிழ்" data-language-local-name="támil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%B5%E0%B0%BF%E0%B0%B8%E0%B1%8D%E0%B0%A4%E0%B1%80%E0%B0%B0%E0%B1%8D%E0%B0%A3%E0%B0%82" title="విస్తీర్ణం – telugu" lang="te" hreflang="te" data-title="విస్తీర్ణం" data-language-autonym="తెలుగు" data-language-local-name="telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%9C%D0%B0%D1%81%D0%BE%D2%B3%D0%B0%D1%82" title="Масоҳат – taxico" lang="tg" hreflang="tg" data-title="Масоҳат" data-language-autonym="Тоҷикӣ" data-language-local-name="taxico" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%9E%E0%B8%B7%E0%B9%89%E0%B8%99%E0%B8%97%E0%B8%B5%E0%B9%88" title="พื้นที่ – tailandés" lang="th" hreflang="th" data-title="พื้นที่" data-language-autonym="ไทย" data-language-local-name="tailandés" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-ti mw-list-item"><a href="https://ti.wikipedia.org/wiki/%E1%8C%BD%E1%8D%8D%E1%88%93%E1%89%B5_%E1%88%98%E1%88%AC%E1%89%B5" title="ጽፍሓት መሬት – tigriña" lang="ti" hreflang="ti" data-title="ጽፍሓት መሬት" data-language-autonym="ትግርኛ" data-language-local-name="tigriña" class="interlanguage-link-target"><span>ትግርኛ</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Sukat" title="Sukat – tagalo" lang="tl" hreflang="tl" data-title="Sukat" 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/Alan" title="Alan – turco" lang="tr" hreflang="tr" data-title="Alan" data-language-autonym="Türkçe" data-language-local-name="turco" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/M%C3%A4ydan" title="Mäydan – tártaro" lang="tt" hreflang="tt" data-title="Mäydan" data-language-autonym="Татарча / tatarça" data-language-local-name="tártaro" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9F%D0%BB%D0%BE%D1%89%D0%B0" title="Площа – ucraíno" lang="uk" hreflang="uk" data-title="Площа" data-language-autonym="Українська" data-language-local-name="ucraíno" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%B1%D9%82%D8%A8%DB%81" title="رقبہ – urdú" lang="ur" hreflang="ur" data-title="رقبہ" data-language-autonym="اردو" data-language-local-name="urdú" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Yuza" title="Yuza – uzbeko" lang="uz" hreflang="uz" data-title="Yuza" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbeko" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Di%E1%BB%87n_t%C3%ADch" title="Diện tích – vietnamita" lang="vi" hreflang="vi" data-title="Diện tích" 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/Ippervlak" title="Ippervlak – West Flemish" lang="vls" hreflang="vls" data-title="Ippervlak" data-language-autonym="West-Vlams" data-language-local-name="West Flemish" class="interlanguage-link-target"><span>West-Vlams</span></a></li><li class="interlanguage-link interwiki-wa mw-list-item"><a href="https://wa.wikipedia.org/wiki/Sitind%C3%AAye" title="Sitindêye – valón" lang="wa" hreflang="wa" data-title="Sitindêye" data-language-autonym="Walon" data-language-local-name="valón" class="interlanguage-link-target"><span>Walon</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Kahaluag" title="Kahaluag – waray-waray" lang="war" hreflang="war" data-title="Kahaluag" data-language-autonym="Winaray" data-language-local-name="waray-waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wo mw-list-item"><a href="https://wo.wikipedia.org/wiki/Yaatuwaay" title="Yaatuwaay – wólof" lang="wo" hreflang="wo" data-title="Yaatuwaay" data-language-autonym="Wolof" data-language-local-name="wólof" class="interlanguage-link-target"><span>Wolof</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E9%9D%A2%E7%A7%AF" title="面积 – chinés wu" lang="wuu" hreflang="wuu" data-title="面积" data-language-autonym="吴语" data-language-local-name="chinés wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%A4%E1%83%90%E1%83%A0%E1%83%97%E1%83%9D%E1%83%91%E1%83%98" title="ფართობი – Mingrelian" lang="xmf" hreflang="xmf" data-title="ფართობი" data-language-autonym="მარგალური" data-language-local-name="Mingrelian" class="interlanguage-link-target"><span>მარგალური</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A9%D7%98%D7%97" title="שטח – yiddish" lang="yi" hreflang="yi" data-title="שטח" data-language-autonym="ייִדיש" data-language-local-name="yiddish" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-yo mw-list-item"><a href="https://yo.wikipedia.org/wiki/%C3%80%C3%A0l%C3%A0" title="Ààlà – ioruba" lang="yo" hreflang="yo" data-title="Ààlà" data-language-autonym="Yorùbá" data-language-local-name="ioruba" class="interlanguage-link-target"><span>Yorùbá</span></a></li><li class="interlanguage-link interwiki-zea mw-list-item"><a href="https://zea.wikipedia.org/wiki/Oppervlak" title="Oppervlak – Zeelandic" lang="zea" hreflang="zea" data-title="Oppervlak" data-language-autonym="Zeêuws" data-language-local-name="Zeelandic" class="interlanguage-link-target"><span>Zeêuws</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E9%9D%A2%E7%A7%AF" title="面积 – chinés" lang="zh" hreflang="zh" data-title="面积" data-language-autonym="中文" data-language-local-name="chinés" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Bi%C4%81n-chek" title="Biān-chek – Minnan" lang="nan" hreflang="nan" data-title="Biān-chek" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E9%9D%A2%E7%A9%8D" title="面積 – cantonés" lang="yue" hreflang="yue" data-title="面積" data-language-autonym="粵語" data-language-local-name="cantonés" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q11500#sitelinks-wikipedia" title="Editar as ligazóns interlingüísticas" class="wbc-editpage">Editar as ligazóns</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="Espazos de nomes"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%C3%81rea" title="Ver o contido da páxina [c]" accesskey="c"><span>Artigo</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Conversa:%C3%81rea&action=edit&redlink=1" rel="discussion" class="new" title="Conversa acerca do contido desta páxina (a páxina aínda non existe) [t]" accesskey="t"><span>Conversa</span></a></li> </ul> 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data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Ferramentas</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">mover á barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">agochar</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Máis opcións" > <div class="vector-menu-heading"> Accións </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/%C3%81rea"><span>Ler</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%C3%81rea&veaction=edit" 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id="siteSub" class="noprint">Na Galipedia, a Wikipedia en galego.</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="gl" dir="ltr"><p class="mw-empty-elt"> </p> <div class="dablink">Para a unidade de superficie véxase: <a href="/wiki/%C3%81rea_(unidade_de_superficie)" title="Área (unidade de superficie)">Área (unidade de superficie)</a>.</div> <p><b>Área</b><sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span>[</span>1<span>]</span></a></sup> é a extensión ou <a href="/wiki/Superficie" title="Superficie">superficie</a> comprendida dentro dunha figura (de dúas <a href="/wiki/Dimensi%C3%B3n" title="Dimensión">dimensións</a>), expresada en unidades de medida denominadas superficiais. Para superficies planas o concepto é intuitivo. Calquera superficie plana de lados rectos pode triangularse e pódese calcular a súa área como suma de triángulos. </p><p>Con todo, para calcular a área de superficies curvas requírese introducir métodos de <a href="/wiki/Xeometr%C3%ADa_diferencial" title="Xeometría diferencial">xeometría diferencial</a>. </p><p>Para poder definir a área dunha superficie en xeral, que é un concepto métrico, tense que definir un tensor métrico sobre a superficie en cuestión: cando a superficie está dentro dun <a href="/wiki/Espazo_euclidiano" title="Espazo euclidiano">espazo euclidiano</a>, a superficie herda unha estrutura métrica natural inducida pola métrica euclídea. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Historia">Historia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%81rea&veaction=edit&section=1" title="Editar a sección: «Historia»" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C3%81rea&action=edit&section=1" title="Editar o código fonte da sección: Historia"><span>editar a fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Ficheiro:Orilla_del_Nilo.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Orilla_del_Nilo.jpg/300px-Orilla_del_Nilo.jpg" decoding="async" width="300" height="161" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Orilla_del_Nilo.jpg/450px-Orilla_del_Nilo.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Orilla_del_Nilo.jpg/600px-Orilla_del_Nilo.jpg 2x" data-file-width="924" data-file-height="495" /></a><figcaption>Os <a href="/wiki/Antigo_Exipto" title="Antigo Exipto">exipcios</a> desenvolveron a xeometría pola necesidade que tiveron de medir as terras á beira do <a href="/wiki/R%C3%ADo_Nilo" class="mw-redirect" title="Río Nilo">río Nilo</a>.</figcaption></figure> <p>A idea de que a área é a medida que proporciona o tamaño da rexión encerrada nunha <a href="/w/index.php?title=Figura_xeom%C3%A9trica&action=edit&redlink=1" class="new" title="Figura xeométrica (a páxina aínda non existe)">figura xeométrica</a> provén da antigüidade. No <a href="/wiki/Antigo_Exipto" title="Antigo Exipto">Antigo Exipto</a>, tras a crecida anual do <a href="/wiki/R%C3%ADo_Nilo" class="mw-redirect" title="Río Nilo">río Nilo</a> inundando os campos, xorde a necesidade de calcular a área de cada parcela agrícola para restablecer os seus límites; para liquidar iso, os exipcios inventaron a <a href="/wiki/Xeometr%C3%ADa" title="Xeometría">xeometría</a>, segundo <a href="/wiki/Her%C3%B3doto" title="Heródoto">Heródoto</a>. Heródoto <i>Historias</i>, Libro II. </p><p>O modo de calcular a área dun polígono como a suma das áreas dos triángulos, é un método que foi proposto por primeira vez polo sabio grego Antifón cara ao ano 430 a. C. Achar a área dunha figura curva entraña máis dificultade. O método de esgotamento consiste en inscribir e circunscribir polígonos na figura xeométrica, aumentar o número de lados de devanditos polígonos e achar a área buscada. Con este sistema, que se coñece como método de exhaución de <a href="/wiki/Eudoxo" class="mw-redirect" title="Eudoxo">Eudoxo</a>, conseguiu achar a fórmula para calcular a área dun <a href="/wiki/C%C3%ADrculo" title="Círculo">círculo</a>. Devandito sistema foi empregado tempo despois por <a href="/wiki/Arquimedes" class="mw-redirect" title="Arquimedes">Arquimedes</a> para resolver outros problemas similares: o problema da área así como o cálculo aproximado do <a href="/wiki/N%C3%BAmero_pi" title="Número pi">número π</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Área_de_figuras_planas"><span id=".C3.81rea_de_figuras_planas"></span>Área de figuras planas</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%81rea&veaction=edit&section=2" title="Editar a sección: «Área de figuras planas»" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C3%81rea&action=edit&section=2" title="Editar o código fonte da sección: Área de figuras planas"><span>editar a fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Área_dun_triángulo"><span id=".C3.81rea_dun_tri.C3.A1ngulo"></span>Área dun triángulo</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%81rea&veaction=edit&section=3" title="Editar a sección: «Área dun triángulo»" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C3%81rea&action=edit&section=3" title="Editar o código fonte da sección: Área dun triángulo"><span>editar a fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A área dun <a href="/wiki/Tri%C3%A1ngulo" title="Triángulo">triángulo</a> calcúlase mediante a seguinte fórmula:<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span>[</span>2<span>]</span></a></sup> </p> <blockquote style="padding: 5px 10px;background-color: white; text-align:left; margin-left:30px; margin-bottom:0.8em; margin-top:0.5em"> <p><br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A={\frac {l\cdot h}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>l</mi> <mo>⋅</mo> <mi>h</mi> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A={\frac {l\cdot h}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/833b77818f36a3c1031497b8f135c1bd79e248cb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:9.389ex; height:5.343ex;" alt="{\displaystyle A={\frac {l\cdot h}{2}}}"></span> </p> </blockquote> <p>onde <i>l</i> é calquera dos lados e <i>h</i> é a altura correspondente a ese lado. </p><p>Se o <a href="/wiki/Tri%C3%A1ngulo#O_triángulo_rectángulo" title="Triángulo">triángulo é rectángulo</a>, a altura coincide cun dos catetos, e a fórmula quedaría da seguinte forma: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A={\frac {a\cdot b}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>a</mi> <mo>⋅</mo> <mi>b</mi> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A={\frac {a\cdot b}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3c48fa15935cd42e88f9d692579f8b94b7d2a4a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:9.584ex; height:5.343ex;" alt="{\displaystyle A={\frac {a\cdot b}{2}}}"></span></dd></dl> <p>onde <b>a</b> e <b>b</b> son os catetos. </p><p>Se o que coñecemos é a lonxitude dos seus lados aplicamos a fórmula de Herón. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S={\sqrt {s(s-a)(s-b)(s-c)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>s</mi> <mo stretchy="false">(</mo> <mi>s</mi> <mo>−</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>s</mi> <mo>−</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>s</mi> <mo>−</mo> <mi>c</mi> <mo stretchy="false">)</mo> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S={\sqrt {s(s-a)(s-b)(s-c)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6596e9344ada420302022229b1d8122cc7a3141c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:28.467ex; height:4.843ex;" alt="{\displaystyle S={\sqrt {s(s-a)(s-b)(s-c)}}}"></span></dd></dl> <p>onde a, b , c son os valores das lonxitudes dos seus lados <i>s</i> = ½ (<i>a</i> + <i>b</i> + <i>c</i>) é o <b>semiperímetro</b> do triángulo. </p><p>Se o triángulo é equilátero, de lado <i>a</i>, a súa área está dada por </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A={\frac {{\sqrt {3}}\cdot a^{2}}{4}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> <mo>⋅</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mn>4</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A={\frac {{\sqrt {3}}\cdot a^{2}}{4}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/458b1e2fa62308ee9807d41841aa78adee9cd5d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:12.739ex; height:5.843ex;" alt="{\displaystyle A={\frac {{\sqrt {3}}\cdot a^{2}}{4}}}"></span> </p> <figure typeof="mw:File/Thumb"><a href="/wiki/Ficheiro:Area.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Area.svg/200px-Area.svg.png" decoding="async" width="200" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Area.svg/300px-Area.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Area.svg/400px-Area.svg.png 2x" data-file-width="800" data-file-height="800" /></a><figcaption>Áreas</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Área_dun_cuadrilátero"><span id=".C3.81rea_dun_cuadril.C3.A1tero"></span>Área dun cuadrilátero</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%81rea&veaction=edit&section=4" title="Editar a sección: «Área dun cuadrilátero»" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C3%81rea&action=edit&section=4" title="Editar o código fonte da sección: Área dun cuadrilátero"><span>editar a fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Ficheiro:Tetragon_measures.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Tetragon_measures.svg/200px-Tetragon_measures.svg.png" decoding="async" width="200" height="222" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Tetragon_measures.svg/300px-Tetragon_measures.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Tetragon_measures.svg/400px-Tetragon_measures.svg.png 2x" data-file-width="324" data-file-height="360" /></a><figcaption>Trapezoide.</figcaption></figure> <ul><li>O <a href="/w/index.php?title=Trapezoide&action=edit&redlink=1" class="new" title="Trapezoide (a páxina aínda non existe)">trapezoide</a> ou cuadrilátero totalmente irregular que ten os seus catro ángulos diferentes e lados de lonxitudes desiguais. Neste caso a área pódese obter mediante <a href="/w/index.php?title=Triangulaci%C3%B3n&action=edit&redlink=1" class="new" title="Triangulación (a páxina aínda non existe)">triangulación</a> sendo:</li></ul> <blockquote style="padding: 5px 10px;background-color: white; text-align:left; margin-left:30px; margin-bottom:0.8em; margin-top:0.5em"> <p><br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A={\frac {a\cdot d\cdot \sin \alpha +b\cdot c\cdot \sin \gamma }{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>a</mi> <mo>⋅</mo> <mi>d</mi> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> <mo>+</mo> <mi>b</mi> <mo>⋅</mo> <mi>c</mi> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mi>γ</mi> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A={\frac {a\cdot d\cdot \sin \alpha +b\cdot c\cdot \sin \gamma }{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d55d005fa088a2c136d7a328cad7a7459febd8f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:28.92ex; height:5.343ex;" alt="{\displaystyle A={\frac {a\cdot d\cdot \sin \alpha +b\cdot c\cdot \sin \gamma }{2}}}"></span> </p> </blockquote> <dl><dd>Sendo: <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/652e1fd9c3a2ca00e1a517783cdbb0e18e4181f8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.875ex; height:1.676ex;" alt="{\displaystyle \alpha \,}"></span> o ángulo comprendido entre os 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\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d73aa5354c24942dab5316be466465a9d171510" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.617ex; height:1.676ex;" alt="{\displaystyle a\,}"></span> 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 d\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f203b686a923982358b9274fb508753ac31b996" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.603ex; height:2.176ex;" alt="{\displaystyle d\,}"></span>.</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \gamma \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>γ</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \gamma \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65da7961fee8269d576e5d06e838bf8695fc5179" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.649ex; height:2.176ex;" alt="{\displaystyle \gamma \,}"></span> o ángulo comprendido entre os 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 b\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b1bcf19f4ec75b1d2cc0be001e58a314fb0a940" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.385ex; height:2.176ex;" alt="{\displaystyle b\,}"></span> 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 c\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8573e7d95140b0d4068258d8162e189563baee6b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.394ex; height:1.676ex;" alt="{\displaystyle c\,}"></span>.</dd></dl></dd></dl> <ul><li>O <a href="/wiki/Rect%C3%A1ngulo" title="Rectángulo">rectángulo</a> é un paralelogramo cuxos ángulos son todos de 90º; a área sería a multiplicación de dúas dos seus lados contiguos <i>a</i> e <i>b</i>:</li></ul> <blockquote style="padding: 5px 10px;background-color: white; text-align:left; margin-left:30px; margin-bottom:0.8em; margin-top:0.5em"> <p><br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A=a\cdot b\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mi>a</mi> <mo>⋅</mo> <mi>b</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A=a\cdot b\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c7fb1d496bd81b9025353be7dff5bd93220ab8d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.135ex; height:2.176ex;" alt="{\displaystyle A=a\cdot b\,}"></span> </p> </blockquote> <ul><li>O <a href="/wiki/Rombo" title="Rombo">rombo</a>, cuxos 4 lados son iguais, ten a súa área dada polo semiproduto das súas dúas diagonais:</li></ul> <blockquote style="padding: 5px 10px;background-color: white; text-align:left; margin-left:30px; margin-bottom:0.8em; margin-top:0.5em"> <p><br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A={\frac {AC\cdot BD}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>A</mi> <mi>C</mi> <mo>⋅</mo> <mi>B</mi> <mi>D</mi> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A={\frac {AC\cdot BD}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/089feae151d8dd5fc9ef04995721bb9ae91eab08" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:14.555ex; height:5.343ex;" alt="{\displaystyle A={\frac {AC\cdot BD}{2}}}"></span> </p> </blockquote> <ul><li>O cadrado é o polígono regular de catro lados, é á vez un rectángulo e un rombo, polo que a súa área pode ser calculada da mesma maneira que a destes dous. En particular, dado que os seus lados son iguais, úsase a fórmula:</li></ul> <blockquote style="padding: 5px 10px;background-color: white; text-align:left; margin-left:30px; margin-bottom:0.8em; margin-top:0.5em"> <p><br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A=a\cdot a\,=a^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mi>a</mi> <mo>⋅</mo> <mi>a</mi> <mspace width="thinmathspace" /> <mo>=</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A=a\cdot a\,=a^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d65b422f2543331be4404812d397fe48b4527c05" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:14.75ex; height:2.676ex;" alt="{\displaystyle A=a\cdot a\,=a^{2}}"></span> </p> </blockquote> <ul><li>Os <a href="/wiki/Paralelogramo" title="Paralelogramo">paralelogramos</a> en xeral teñen a súa área dada polo produto un dos seus lados e a súa <a href="/wiki/Altura_(magnitude)" title="Altura (magnitude)">altura</a> respectiva:</li></ul> <blockquote style="padding: 5px 10px;background-color: white; text-align:left; margin-left:30px; margin-bottom:0.8em; margin-top:0.5em"> <p><br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A=b\cdot h\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mi>b</mi> <mo>⋅</mo> <mi>h</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A=b\cdot h\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/55194182f084f83d761e6b25f6b479b6470f9540" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.244ex; height:2.176ex;" alt="{\displaystyle A=b\cdot h\,}"></span> </p> </blockquote> <ul><li>O <a href="/wiki/Trapecio" title="Trapecio">trapecio</a> (que ten dous lados paralelos entre si e dous lados non paralelos) cuxa área vén dada pola media aritmética dos seus lados paralelos multiplicado pola distancia entre eles (altura):</li></ul> <blockquote style="padding: 5px 10px;background-color: white; text-align:left; margin-left:30px; margin-bottom:0.8em; margin-top:0.5em"> <p><br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A={\frac {a+b}{2}}\cdot h}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>a</mi> <mo>+</mo> <mi>b</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>⋅</mo> <mi>h</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A={\frac {a+b}{2}}\cdot h}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/88acc4bc72f097ef27daf84e7773366abe9b27a1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:13.764ex; height:5.343ex;" alt="{\displaystyle A={\frac {a+b}{2}}\cdot h}"></span> </p> </blockquote> <div class="mw-heading mw-heading3"><h3 id="Área_do_círculo_e_a_elipse"><span id=".C3.81rea_do_c.C3.ADrculo_e_a_elipse"></span>Área do círculo e a elipse</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%81rea&veaction=edit&section=5" title="Editar a sección: «Área do círculo e a elipse»" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C3%81rea&action=edit&section=5" title="Editar o código fonte da sección: Área do círculo e a elipse"><span>editar a fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A área dun <a href="/wiki/C%C3%ADrculo" title="Círculo">círculo</a>, ou a delimitada por unha <a href="/wiki/Circunferencia" title="Circunferencia">circunferencia</a>, calcúlase mediante a seguinte expresión matemática: </p> <blockquote style="padding: 5px 10px;background-color: white; text-align:left; margin-left:30px; margin-bottom:0.8em; margin-top:0.5em"> <p><br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A=\pi \cdot r^{2}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mi>π</mi> <mo>⋅</mo> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A=\pi \cdot r^{2}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32500ea988d7b421d35e937dd666f34f630a5562" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.343ex; height:2.676ex;" alt="{\displaystyle A=\pi \cdot r^{2}\,}"></span> </p> </blockquote> <figure typeof="mw:File/Thumb"><a href="/wiki/Ficheiro:Areabetweentwographs.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Areabetweentwographs.svg/200px-Areabetweentwographs.svg.png" decoding="async" width="200" height="180" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Areabetweentwographs.svg/300px-Areabetweentwographs.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Areabetweentwographs.svg/400px-Areabetweentwographs.svg.png 2x" data-file-width="1000" data-file-height="900" /></a><figcaption>A área delimitada entre a gráfica de dúas curvas pode calcularse mediante a diferenza entre as integrais de ambas as funcións.</figcaption></figure> <p>A área delimitada por unha <a href="/wiki/Elipse_(xeometr%C3%ADa)" title="Elipse (xeometría)">elipse</a> é similar e obtense como produto do semieixe maior polo semieixe menor multiplicados por π: </p> <blockquote style="padding: 5px 10px;background-color: white; text-align:left; margin-left:30px; margin-bottom:0.8em; margin-top:0.5em"> <p><br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A=\pi \cdot a\cdot b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mi>π</mi> <mo>⋅</mo> <mi>a</mi> <mo>⋅</mo> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A=\pi \cdot a\cdot b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bbf387609ab650f11ae76cb282b826f633d65253" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.759ex; height:2.176ex;" alt="{\displaystyle A=\pi \cdot a\cdot b}"></span> </p> </blockquote> <div class="mw-heading mw-heading3"><h3 id="Área_delimitada_entre_dúas_funcións"><span id=".C3.81rea_delimitada_entre_d.C3.BAas_funci.C3.B3ns"></span>Área delimitada entre dúas funcións</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%81rea&veaction=edit&section=6" title="Editar a sección: «Área delimitada entre dúas funcións»" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C3%81rea&action=edit&section=6" title="Editar o código fonte da sección: Área delimitada entre dúas funcións"><span>editar a fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Unha forma para achar a área delimitada entre dúas <a href="/wiki/Funci%C3%B3n_matem%C3%A1tica" class="mw-redirect" title="Función matemática">funcións</a>, é utilizando o <a href="/wiki/Integral" title="Integral">cálculo integral</a>: </p> <blockquote style="padding: 5px 10px;background-color: white; text-align:left; margin-left:30px; margin-bottom:0.8em; margin-top:0.5em"> <p><br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A(a,b)=\int _{a}^{b}|f(x)-g(x)|dx}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>g</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>d</mi> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A(a,b)=\int _{a}^{b}|f(x)-g(x)|dx}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/26a7107f1afaacca7c341db037db1310633572b1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:29.053ex; height:6.343ex;" alt="{\displaystyle A(a,b)=\int _{a}^{b}|f(x)-g(x)|dx}"></span> </p> </blockquote> <p>O resultado desta integral é a área comprendida entre as curvas: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78b2b66021c2cac2b5654495678c63ff142952e5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.805ex; height:2.843ex;" alt="{\displaystyle f(x)\,}"></span> 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 g(x)[<f(x)]\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>g</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">[</mo> <mo><</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">]</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g(x)[<f(x)]\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a064a1435425a7eb665051170c682abc37bb7545" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.807ex; height:2.843ex;" alt="{\displaystyle g(x)[<f(x)]\,}"></span> no intervalo <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle [a,b]\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">]</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [a,b]\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/23cb97ebba2cd3175f9a77446963c1849fc353ee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.942ex; height:2.843ex;" alt="{\displaystyle [a,b]\,}"></span>. </p> <dl><dt>Exemplo</dt></dl> <p>Se se quere achar a área delimitada entre o eixo x e a función f(x) = 4 - x^2 no intervalo [-2;2], utilízase a ecuación anterior, neste caso: g(x)=0 entón avaliando a integral, obtense: </p> <blockquote style="padding: 5px 10px;background-color: white; text-align:left; margin-left:30px; margin-bottom:0.8em; margin-top:0.5em"> <p><br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A(-2,2)=\int _{-2}^{2}|4-x^{2}-0|dx=2\int _{0}^{2}4-x^{2}dx=2\left[8-\left({\frac {2^{3}-0}{3}}\right)\right]={\frac {32}{3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo stretchy="false">(</mo> <mo>−</mo> <mn>2</mn> <mo>,</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mn>4</mn> <mo>−</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>0</mn> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mn>2</mn> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mn>4</mn> <mo>−</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mn>2</mn> <mrow> <mo>[</mo> <mrow> <mn>8</mn> <mo>−</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>−</mo> <mn>0</mn> </mrow> <mn>3</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mo>]</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>32</mn> <mn>3</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A(-2,2)=\int _{-2}^{2}|4-x^{2}-0|dx=2\int _{0}^{2}4-x^{2}dx=2\left[8-\left({\frac {2^{3}-0}{3}}\right)\right]={\frac {32}{3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/842be32fdbb63e90b93ff7261cbc76d9b1cdbb0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:75.387ex; height:6.343ex;" alt="{\displaystyle A(-2,2)=\int _{-2}^{2}|4-x^{2}-0|dx=2\int _{0}^{2}4-x^{2}dx=2\left[8-\left({\frac {2^{3}-0}{3}}\right)\right]={\frac {32}{3}}}"></span> </p> </blockquote> <p>Polo que se conclúe que a área delimitada é <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {32}{3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>32</mn> <mn>3</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {32}{3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8d0c521bac8c28d0cca31f4e96d1368a88bb7856" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:3.161ex; height:5.176ex;" alt="{\displaystyle {\frac {32}{3}}}"></span>.. </p><p>O <a href="/wiki/Volume_(f%C3%ADsica)" class="mw-redirect" title="Volume (física)">volume</a> encerrado entre dúas funcións tamén pode ser reducido ao cálculo dunha integral, similar. </p> <div class="mw-heading mw-heading2"><h2 id="Área_de_superficies_curvas"><span id=".C3.81rea_de_superficies_curvas"></span>Área de superficies curvas</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%81rea&veaction=edit&section=7" title="Editar a sección: «Área de superficies curvas»" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C3%81rea&action=edit&section=7" title="Editar o código fonte da sección: Área de superficies curvas"><span>editar a 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:Cone_3d.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Cone_3d.png/220px-Cone_3d.png" decoding="async" width="220" height="110" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Cone_3d.png/330px-Cone_3d.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Cone_3d.png/440px-Cone_3d.png 2x" data-file-width="913" data-file-height="458" /></a><figcaption>Dous exemplos de <a href="/wiki/Cono" title="Cono">conos</a>.</figcaption></figure> <p>A área dunha superficie curva é máis complexo e en xeral supón realizar algún tipo de idealización ou límite para medilo. </p> <ul><li>Cando a superficie é desenvolvíbel, como sucede coa área lateral dun <a href="/wiki/Cilindro" title="Cilindro">cilindro</a> ou dun <a href="/wiki/Cono" title="Cono">cono</a> a área da superficie pode calcularse a partir da área desenvolvida que sempre é unha figura plana. Unha condición matemática necesaria para que unha superficie sexa desenvolvíbel é que a súa curvatura gaussiana sexa nula.</li> <li>Cando a superficie non é desenvolvíbel, o cálculo da superficie ou a fórmula analítica para atopar devandito valor é máis traballoso. Un exemplo de superficie non desenvolvíbel é a <a href="/wiki/Esfera" title="Esfera">esfera</a> xa que a súa curvatura gaussiana coincide co inverso do seu radio ao cadrado, e por tanto non é cero. Con todo a esfera é unha superficie de revolución.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Superficie_de_revolución"><span id="Superficie_de_revoluci.C3.B3n"></span>Superficie de revolución</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%81rea&veaction=edit&section=8" title="Editar a sección: «Superficie de revolución»" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C3%81rea&action=edit&section=8" title="Editar o código fonte da sección: Superficie de revolución"><span>editar a fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Ficheiro:Surface_of_revolution_illustration.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Surface_of_revolution_illustration.png/200px-Surface_of_revolution_illustration.png" decoding="async" width="200" height="255" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Surface_of_revolution_illustration.png/300px-Surface_of_revolution_illustration.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Surface_of_revolution_illustration.png/400px-Surface_of_revolution_illustration.png 2x" data-file-width="693" data-file-height="885" /></a><figcaption>Unha superficie de revolución xerada por un tramo da curva <i>y</i>=2+cos <i>x</i> rotada arredor do eixo <i>x</i>.</figcaption></figure> <p>Cando unha superficie curva pode ser xerada facendo virar unha curva plana ao redor dun eixo <a href="/w/index.php?title=Directriz&action=edit&redlink=1" class="new" title="Directriz (a páxina aínda non existe)">directriz</a>, a superficie resultante chámase <a href="/w/index.php?title=Superficie_de_revoluci%C3%B3n&action=edit&redlink=1" class="new" title="Superficie de revolución (a páxina aínda non existe)">superficie de revolución</a> e a súa área pode ser calculada facilmente a partir da lonxitude da curva xeratriz que ao virar conforma a superficie. Se <i>y</i>=<i>f</i>(<i>x</i>) é a ecuación que define un tramo de curva, ao virar esta curva ao redor do eixo X xérase unha superficie de revolución cuxa área lateral vale: </p> <blockquote style="padding: 5px 10px;background-color: white; text-align:left; margin-left:30px; margin-bottom:0.8em; margin-top:0.5em"> <p><br /> <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_{r}(a,b)=2\pi \int _{a}^{b}f(x){\sqrt {1+\left({\frac {df(x)}{dx}}\right)^{2}}}\ dx}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>2</mn> <mi>π</mi> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msubsup> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>1</mn> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>d</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mtext> </mtext> <mi>d</mi> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{r}(a,b)=2\pi \int _{a}^{b}f(x){\sqrt {1+\left({\frac {df(x)}{dx}}\right)^{2}}}\ dx}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92bc9778585e9f3eb424f0ebc3b47ff0551ea982" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:42.372ex; height:7.509ex;" alt="{\displaystyle A_{r}(a,b)=2\pi \int _{a}^{b}f(x){\sqrt {1+\left({\frac {df(x)}{dx}}\right)^{2}}}\ dx}"></span> </p> </blockquote> <div class="mw-heading mw-heading3"><h3 id="Cálculo_xeral_de_áreas"><span id="C.C3.A1lculo_xeral_de_.C3.A1reas"></span>Cálculo xeral de áreas</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%81rea&veaction=edit&section=9" title="Editar a sección: «Cálculo xeral de áreas»" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C3%81rea&action=edit&section=9" title="Editar o código fonte da sección: Cálculo xeral de áreas"><span>editar a fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Mediante a xeometría diferencial de superficies ou máis xeralmente a xeometría riemanniana pode calcularse a área de calquera superficie curva finita. Se a superficie vén dada pola función explícita <i>z</i> = <i>f</i>(<i>x, y</i>) entón, dada unha rexión Ω contida nunha superficie a súa área resultar ser: </p> <blockquote style="padding: 5px 10px;background-color: white; text-align:left; margin-left:30px; margin-bottom:0.8em; margin-top:0.5em"> <p><br /> <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(\Omega )=\iint _{\Omega }{\sqrt {1+\left({\frac {\partial f}{\partial x}}\right)^{2}+\left({\frac {\partial f}{\partial y}}\right)^{2}}}dxdy}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo stretchy="false">(</mo> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mo>∬</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Ω</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>1</mn> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>f</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>f</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>y</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mi>d</mi> <mi>x</mi> <mi>d</mi> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A(\Omega )=\iint _{\Omega }{\sqrt {1+\left({\frac {\partial f}{\partial x}}\right)^{2}+\left({\frac {\partial f}{\partial y}}\right)^{2}}}dxdy}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/16ca0f177480e5f94064249a6ecfa355031dbffd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:42.605ex; height:7.676ex;" alt="{\displaystyle A(\Omega )=\iint _{\Omega }{\sqrt {1+\left({\frac {\partial f}{\partial x}}\right)^{2}+\left({\frac {\partial f}{\partial y}}\right)^{2}}}dxdy}"></span> </p> </blockquote> <p>De maneira un pouco máis xeral se coñecemos a ecuación paramétrica da superficie en función de dúas coordenadas calquera <i>o</i> e <i>v</i> entón a área anterior pode escribirse como: </p> <blockquote style="padding: 5px 10px;background-color: white; text-align:left; margin-left:30px; margin-bottom:0.8em; margin-top:0.5em"> <p><br /> <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(\Omega )=\iint _{\Omega }{\sqrt {EG-F^{2}}}\ dudv}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo stretchy="false">(</mo> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mo>∬</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Ω</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>E</mi> <mi>G</mi> <mo>−</mo> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mtext> </mtext> <mi>d</mi> <mi>u</mi> <mi>d</mi> <mi>v</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A(\Omega )=\iint _{\Omega }{\sqrt {EG-F^{2}}}\ dudv}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/979404c240be0485a52b4a372b1552d92925990e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:29.759ex; height:5.676ex;" alt="{\displaystyle A(\Omega )=\iint _{\Omega }{\sqrt {EG-F^{2}}}\ dudv}"></span> </p> </blockquote> <p>Onde <i>E</i>, <i>F</i> e <i>G</i> son as compoñentes do tensor métrico ou primeira forma fundamental da superficie nas coordenadas paramétricas <i>u</i> e <i>v</i>. </p> <div class="mw-heading mw-heading2"><h2 id="Unidades_de_medida_de_superficies">Unidades de medida de superficies</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%81rea&veaction=edit&section=10" title="Editar a sección: «Unidades de medida de superficies»" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C3%81rea&action=edit&section=10" title="Editar o código fonte da sección: Unidades de medida de superficies"><span>editar a fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="detail principal"> <dl><dd><span><span><i>Artigo principal</i><i>:</i> <a href="/wiki/Unidade_de_superficie" title="Unidade de superficie">Unidade de superficie</a>.</span></span></dd></dl></div> <div class="mw-heading mw-heading3"><h3 id="Sistema_métrico_(SI)"><span id="Sistema_m.C3.A9trico_.28SI.29"></span>Sistema métrico (<a href="/wiki/Sistema_Internacional_de_Unidades" title="Sistema Internacional de Unidades">SI</a>)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%81rea&veaction=edit&section=11" title="Editar a sección: «Sistema métrico (SI)»" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C3%81rea&action=edit&section=11" title="Editar o código fonte da sección: Sistema métrico (SI)"><span>editar a fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Múltiplos:</b> </p> <ul><li><a href="/wiki/Quil%C3%B3metro_cadrado" title="Quilómetro cadrado">Quilómetro cadrado</a>: 10<sup>6</sup> metros cadrados</li> <li><a href="/wiki/Hect%C3%A1rea" title="Hectárea">Hectárea</a>: 10<sup>4</sup> metros cadrados</li> <li><a href="/wiki/%C3%81rea_(unidade_de_superficie)" title="Área (unidade de superficie)">Área</a>: 10² metros cadrados</li></ul> <p><b>Unidade básica:</b> </p> <ul><li><a href="/wiki/Metro_cadrado" title="Metro cadrado">metro cadrado</a>: Unidade derivada do <a href="/wiki/SI" class="mw-redirect" title="SI">SI</a></li></ul> <p><b>Submúltiplos:</b> </p> <ul><li><a href="/wiki/Cent%C3%ADmetro_cadrado" title="Centímetro cadrado">centímetro cadrado</a>: 10<sup>−4</sup> metros cadrados</li> <li><a href="/wiki/Barn" title="Barn">barn</a>: 10<sup>−28</sup> metros cadrados</li></ul> <div class="mw-heading mw-heading3"><h3 id="Sistema_inglés_de_medidas"><span id="Sistema_ingl.C3.A9s_de_medidas"></span>Sistema inglés de medidas</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%81rea&veaction=edit&section=12" title="Editar a sección: «Sistema inglés de medidas»" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C3%81rea&action=edit&section=12" title="Editar o código fonte da sección: Sistema inglés de medidas"><span>editar a fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/w/index.php?title=Polgada_cadrada&action=edit&redlink=1" class="new" title="Polgada cadrada (a páxina aínda non existe)">polgada cadrada</a></li> <li><a href="/wiki/P%C3%A9_cadrado" title="Pé cadrado">pé cadrado</a></li> <li><a href="/w/index.php?title=Iarda_cadrada&action=edit&redlink=1" class="new" title="Iarda cadrada (a páxina aínda non existe)">iarda cadrada</a></li> <li><a href="/wiki/Acre_(unidade_de_superficie)" title="Acre (unidade de superficie)">acre</a></li> <li><a href="/w/index.php?title=Milla_cadrada&action=edit&redlink=1" class="new" title="Milla cadrada (a páxina aínda non existe)">milla cadrada</a></li> <li><a href="/w/index.php?title=Legua_cadrada&action=edit&redlink=1" class="new" title="Legua cadrada (a páxina aínda non existe)">legua cadrada</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notas">Notas</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%81rea&veaction=edit&section=13" title="Editar a sección: «Notas»" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C3%81rea&action=edit&section=13" title="Editar o código fonte da sección: Notas"><span>editar a fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist" style="list-style-type: decimal;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">Definicións no <a rel="nofollow" class="external text" href="http://academia.gal/dicionario/-/termo/%C3%A1rea"><i>Dicionario da Real Academia Galega</i></a> e no <a rel="nofollow" class="external text" href="http://portaldaspalabras.gal/dicionario/procura/%C3%A1rea">Portal das Palabras</a> para <i>área</i>.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text">Spiegel y Abellanas, 1992, p.9</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Véxase_tamén"><span id="V.C3.A9xase_tam.C3.A9n"></span>Véxase tamén</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%81rea&veaction=edit&section=14" title="Editar a sección: «Véxase tamén»" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C3%81rea&action=edit&section=14" title="Editar o código fonte da sección: Véxase tamén"><span>editar a fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <table role="presentation" class="mbox-small plainlinks sistersitebox" style="background-color:var(--background-color-neutral-subtle, #f8f9fa);border:1px solid var(--border-color-base, #a2a9b1);color:inherit"> <tbody><tr> <td class="mbox-image"><span class="noviewer" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></td> <td class="mbox-text plainlist"><a href="https://commons.wikimedia.org/wiki/Portada_galega" class="extiw" title="commons:Portada galega">Wikimedia Commons</a> ten máis contidos multimedia na categoría:  <i><b><a href="https://commons.wikimedia.org/wiki/Category:Area" class="extiw" title="commons:Category:Area">Área</a> <span typeof="mw:File"><a href="https://www.wikidata.org/wiki/Q11500" title="Modificar a ligazón no Wikidata"><img alt="Modificar a ligazón no Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/12px-Arbcom_ru_editing.svg.png" decoding="async" width="12" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/18px-Arbcom_ru_editing.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/24px-Arbcom_ru_editing.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span></b></i></td></tr> </tbody></table> <div class="mw-heading mw-heading3"><h3 id="Bibliografía"><span id="Bibliograf.C3.ADa"></span>Bibliografía</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%81rea&veaction=edit&section=15" title="Editar a sección: «Bibliografía»" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C3%81rea&action=edit&section=15" title="Editar o código fonte da sección: Bibliografía"><span>editar a fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><cite class="citation book">Spiegel, Murray R.; Abellanas, Lorenzo. McGraw-Hill, ed. <i>Fórmulas y tablas de matemática aplicada</i>. Aravaca (Madrid). <a href="/wiki/Especial:Fontes_bibliogr%C3%A1ficas/8476151977" class="internal mw-magiclink-isbn">ISBN 84-7615-197-7</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fgl.wikipedia.org%3A%C3%81rea&rft.au=Abellanas%2C+Lorenzo&rft.au=Spiegel%2C+Murray+R.&rft.btitle=F%C3%B3rmulas+y+tablas+de+matem%C3%A1tica+aplicada&rft.genre=book&rft.place=Aravaca+%28Madrid%29&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span> </p> <div role="navigation" class="navbox" aria-labelledby="Control_de_autoridades" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th id="Control_de_autoridades" scope="row" class="navbox-group" style="width:1%;width: 12%; text-align:center;"><a href="/wiki/Axuda:Control_de_autoridades" title="Axuda:Control de autoridades">Control de autoridades</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/Q11500" class="extiw" title="wikidata:Q11500">Q11500</a></span></span></li> <li><span style="white-space:nowrap;"><a href="/wiki/Biblioteca_Nacional_Central_de_Florencia" title="Biblioteca Nacional Central de Florencia">BNCF</a>: <span class="uid"><span class="plainlinks"><a rel="nofollow" class="external text" href="https://thes.bncf.firenze.sbn.it/termine.php?id=39330">39330</a></span></span></span></li> <li><span style="white-space:nowrap;"><a href="/wiki/Biblioteca_Nacional_de_Francia" title="Biblioteca Nacional de Francia">BNF</a>: <span class="uid"><span class="plainlinks"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb12172891w">12172891w</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/4193807-0">4193807-0</a></span></span></span></li> <li><span style="white-space:nowrap;"><a href="/wiki/Library_of_Congress_Control_Number" title="Library of Congress Control Number">LCCN</a>: <span class="uid"><span class="plainlinks"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/sh85006984">sh85006984</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; 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