{"id":150426,"date":"2025-11-28T18:13:57","date_gmt":"2025-11-28T21:13:57","guid":{"rendered":"https:\/\/vestibulares.estrategia.com\/portal\/?p=150426"},"modified":"2026-01-23T17:59:54","modified_gmt":"2026-01-23T20:59:54","slug":"area-do-triangulo-curvilineo-definicao-exercicios-e-aplicacoes","status":"publish","type":"post","link":"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/area-do-triangulo-curvilineo-definicao-exercicios-e-aplicacoes\/","title":{"rendered":"\u00c1rea do tri\u00e2ngulo curvil\u00edneo: defini\u00e7\u00e3o, exerc\u00edcios e aplica\u00e7\u00f5es\u00a0"},"content":{"rendered":"<p>Entre os diversos temas de geometria plana que aparecem em provas de vestibulares e no Enem, um dos mais intrigantes &eacute; o chamado &ldquo;tri&acirc;ngulo curvil&iacute;neo&rdquo;. Diferente de figuras tradicionais, como tri&acirc;ngulos e quadrados, que possuem defini&ccedil;&otilde;es r&iacute;gidas e f&oacute;rmulas conhecidas, o tri&acirc;ngulo curvil&iacute;neo &eacute; uma figura que depende de constru&ccedil;&otilde;es espec&iacute;ficas.<p>N&atilde;o existe uma f&oacute;rmula &uacute;nica para calcular sua &aacute;rea. O segredo est&aacute; em decompor a regi&atilde;o em &aacute;reas conhecidas (tri&acirc;ngulos, setores e segmentos circulares) e depois somar ou subtrair de forma estrat&eacute;gica. &Eacute; um tema que exige racioc&iacute;nio geom&eacute;trico e habilidade de visualiza&ccedil;&atilde;o, mas que pode ser dominado com pr&aacute;tica. Leia este texto para aprender a resolver as principais quest&otilde;es sobre o tema. Vamos l&aacute;?<\/p><p>\n\n\n\n<a id=\"cta\" class=\"cta-imagem\" href=\"https:\/\/vestibulares.estrategia.com\/curso\/pacote-enem\/\" target=\"blank\">\n                <img decoding=\"async\" width=\"100%\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2021\/12\/Enem.jpg\" alt=\"CTA curso Enem\" title=\"CTA curso Enem\">\n        <\/a>\n\n\n\n<\/p><div id=\"ez-toc-container\" class=\"ez-toc-v2_0_76 counter-hierarchy ez-toc-counter ez-toc-transparent ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\"><p class=\"ez-toc-title\" style=\"cursor:inherit\">Navegue pelo conte\u00fado<\/p>\n<\/div><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/area-do-triangulo-curvilineo-definicao-exercicios-e-aplicacoes\/#O-que-e-um-triangulo-curvilineo\" >O que &eacute; um tri&acirc;ngulo curvil&iacute;neo?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/area-do-triangulo-curvilineo-definicao-exercicios-e-aplicacoes\/#Calculo-da-area-de-um-triangulo-curvilineo\" >C&aacute;lculo da &aacute;rea de um tri&acirc;ngulo curvil&iacute;neo<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/area-do-triangulo-curvilineo-definicao-exercicios-e-aplicacoes\/#Requisitos-essenciais-no-calculo-de-triangulos-curvilineos\" >Requisitos essenciais no c&aacute;lculo de tri&acirc;ngulos curvil&iacute;neos<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/area-do-triangulo-curvilineo-definicao-exercicios-e-aplicacoes\/#Exercicios-de-fixacao\" >Exerc&iacute;cios de fixa&ccedil;&atilde;o<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/area-do-triangulo-curvilineo-definicao-exercicios-e-aplicacoes\/#Erros-comuns-no-calculo-da-area-de-triangulos-curvilineos\" >Erros comuns no c&aacute;lculo da &aacute;rea de tri&acirc;ngulos curvil&iacute;neos<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/area-do-triangulo-curvilineo-definicao-exercicios-e-aplicacoes\/#Estude-com-o-Estrategia-Vestibulares\" >Estude com o Estrat&eacute;gia Vestibulares<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\" id=\"h-o-que-e-um-triangulo-curvilineo\"><span class=\"ez-toc-section\" id=\"O-que-e-um-triangulo-curvilineo\"><\/span>O que &eacute; um tri&acirc;ngulo curvil&iacute;neo?<span class=\"ez-toc-section-end\"><\/span><\/h2><p>O termo tri&acirc;ngulo curvil&iacute;neo n&atilde;o se refere a um tri&acirc;ngulo comum. Ele designa uma regi&atilde;o delimitada por tr&ecirc;s arcos de circunfer&ecirc;ncia, que se encontram em tr&ecirc;s pontos, formando uma esp&eacute;cie de &ldquo;tri&acirc;ngulo de lados arredondados&rdquo;.<\/p><p>Visualmente, imagine um tri&acirc;ngulo tradicional, mas em vez de lados retos, cada lado &eacute; substitu&iacute;do por um arco de circunfer&ecirc;ncia. O resultado &eacute; uma figura com tr&ecirc;s v&eacute;rtices (onde os arcos se encontram) e tr&ecirc;s lados curvos.<\/p><h2 class=\"wp-block-heading\" id=\"h-calculo-da-area-de-um-triangulo-curvilineo\"><span class=\"ez-toc-section\" id=\"Calculo-da-area-de-um-triangulo-curvilineo\"><\/span>C&aacute;lculo da &aacute;rea de um tri&acirc;ngulo curvil&iacute;neo<span class=\"ez-toc-section-end\"><\/span><\/h2><p>N&atilde;o existe uma f&oacute;rmula direta para calcularmos a &aacute;rea de um tri&acirc;ngulo curvil&iacute;neo. O que faremos para descobrir a &aacute;rea dessa figura &eacute; somar e subtrair &aacute;reas conhecidas. Pode parecer um pouco confuso &agrave; primeira vista, mas, ao decorrer do texto, a ideia ficar&aacute; mais clara.<\/p><p>Portanto, &eacute; necess&aacute;rio ter conhecimento das f&oacute;rmulas para calcular a &aacute;rea de tri&acirc;ngulos, &aacute;rea de setores circulares e &aacute;rea de segmentos circulares. Mas, existem algumas configura&ccedil;&otilde;es comuns de tri&acirc;ngulos curvil&iacute;neos, para as quais podemos elaborar f&oacute;rmulas que facilitem o c&aacute;lculo da &aacute;rea dessas figuras geom&eacute;tricas.<\/p><h3 class=\"wp-block-heading\" id=\"h-triangulo-curvilineo-formado-entre-tres-circunferencias-tangentes\">Tri&acirc;ngulo curvil&iacute;neo formado entre tr&ecirc;s circunfer&ecirc;ncias tangentes<\/h3><p>Uma situa&ccedil;&atilde;o cl&aacute;ssica &eacute; a seguinte: temos tr&ecirc;s circunfer&ecirc;ncias externas, mutuamente tangentes, com <strong>raios r<\/strong><strong><sub>1<\/sub><\/strong><strong>, r<\/strong><strong><sub>2<\/sub><\/strong><strong> e r<\/strong><strong><sub>3<\/sub><\/strong>. A regi&atilde;o delimitada pelos tr&ecirc;s arcos de tang&ecirc;ncia forma o tri&acirc;ngulo curvil&iacute;neo. Para calcular a &aacute;rea nesses casos:<\/p><ul class=\"wp-block-list\">\n<li>Construa o tri&acirc;ngulo dos centros das circunfer&ecirc;ncias, sabendo que os v&eacute;rtices desse tri&acirc;ngulo s&atilde;o os centros das tr&ecirc;s circunfer&ecirc;ncias e os lados s&atilde;o r<sub>1<\/sub>, r<sub>2<\/sub> e r<sub>3<\/sub>;<\/li>\n<\/ul><ul class=\"wp-block-list\">\n<li>Calcule a &aacute;rea desse tri&acirc;ngulo; e<\/li>\n\n\n\n<li>Subtraia as &aacute;reas dos setores circulares.<\/li>\n<\/ul><p>Cada circunfer&ecirc;ncia delimita um setor circular na regi&atilde;o central. O &acirc;ngulo de cada setor &eacute; justamente o &acirc;ngulo interno do tri&acirc;ngulo dos centros. Assim, a &aacute;rea final &eacute;:<\/p><p>A<sub>curvil&iacute;neo<\/sub> = A<sub>tri&acirc;ngulo dos centros<\/sub> &ndash; (A<sub>setor 1<\/sub> + A<sub>setor 2<\/sub> + A<sub>setor 3<\/sub>)<\/p><h4 class=\"wp-block-heading\" id=\"h-caso-particular-raios-iguais-r1-r2-r3\">Caso particular: raios iguais (r1 = r2 = r3)<\/h4><p>Nesse caso, o tri&acirc;ngulo dos centros &eacute; equil&aacute;tero, com lado 2r. Portanto, a &aacute;rea do tri&acirc;ngulo &eacute;:<\/p><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"176\" height=\"47\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/11\/image-1-55.png\" alt=\"\" class=\"wp-image-150453\"><\/figure><\/div><p>Al&eacute;m disso, como o tri&acirc;ngulo &eacute; equil&aacute;tero, cada &acirc;ngulo interno &eacute; de 60&deg;, logo cada setor tem &aacute;rea:<\/p><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"160\" height=\"50\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/11\/image-1-56.png\" alt=\"\" class=\"wp-image-150456\"><\/figure><\/div><p> Assim, os tr&ecirc;s setores juntos somam &pi;r<sup>2<\/sup>\/2.<\/p><p><strong>Portanto:<\/strong><\/p><p>A<sub>curvil&iacute;neo<\/sub>:<\/p><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"105\" height=\"50\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/11\/image-1-57.png\" alt=\"\" class=\"wp-image-150458\"><\/figure><\/div><h3 class=\"wp-block-heading\" id=\"h-triangulo-com-arcos-nos-vertices\">Tri&acirc;ngulo com arcos nos v&eacute;rtices<\/h3><p>Outra configura&ccedil;&atilde;o comum em vestibulares &eacute; a seguinte: dentro de um tri&acirc;ngulo equil&aacute;tero, tra&ccedil;am-se arcos de circunfer&ecirc;ncia com centro nos v&eacute;rtices, geralmente com raio igual &agrave; metade do lado do tri&acirc;ngulo. A regi&atilde;o central, delimitada pelos tr&ecirc;s arcos, &eacute; o tri&acirc;ngulo curvil&iacute;neo. Para calcular a &aacute;rea do tri&acirc;ngulo curvil&iacute;neo nesses casos:<\/p><ul class=\"wp-block-list\">\n<li>Calcule a &aacute;rea do tri&acirc;ngulo equil&aacute;tero: A<sub>equil&aacute;tero<\/sub> = <img decoding=\"async\" width=\"39\" height=\"28\" src=\"data:image\/png;base64,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\">;<\/li>\n\n\n\n<li>Determine a &aacute;rea de cada setor circular: cada setor tem raio l\/2 e &acirc;ngulo de 60&deg;. Logo, cada setor tem &aacute;rea: A<sub>setor<\/sub> = <img decoding=\"async\" width=\"129\" height=\"34\" src=\"data:image\/png;base64,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\">; e<\/li>\n\n\n\n<li>Subtraia a soma dos setores do tri&acirc;ngulo: Como s&atilde;o tr&ecirc;s setores: A<sub>setores<\/sub> = <img decoding=\"async\" width=\"83\" height=\"39\" src=\"data:image\/png;base64,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\">.<\/li>\n<\/ul><p>Dessa maneira, encontramos a f&oacute;rmula a &aacute;rea de um tri&acirc;ngulo curvil&iacute;neo interno a um tri&acirc;ngulo equil&aacute;tero:<\/p><p>A<sub>curvil&iacute;neo<\/sub> = A<sub>equil&aacute;tero<\/sub> &ndash; A<sub>setores<\/sub><\/p><p>A<sub>curvil&iacute;neo<\/sub>:<\/p><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"346\" height=\"54\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/11\/image-1-58.png\" alt=\"\" class=\"wp-image-150460\"><\/figure><\/div><h2 class=\"wp-block-heading\" id=\"h-requisitos-essenciais-no-calculo-de-triangulos-curvilineos\"><span class=\"ez-toc-section\" id=\"Requisitos-essenciais-no-calculo-de-triangulos-curvilineos\"><\/span>Requisitos essenciais no c&aacute;lculo de tri&acirc;ngulos curvil&iacute;neos<span class=\"ez-toc-section-end\"><\/span><\/h2><p>Para lidar com tri&acirc;ngulos curvil&iacute;neos com seguran&ccedil;a, o estudante precisa dominar tr&ecirc;s blocos fundamentais da Geometria Plana. Veja-os abaixo:<\/p><h3 class=\"wp-block-heading\" id=\"h-areas-de-triangulos-nbsp\">&Aacute;reas de tri&acirc;ngulos&nbsp;<\/h3><p>Para resolver problemas de regi&otilde;es delimitadas por arcos, &eacute; essencial saber calcular &aacute;reas de tri&acirc;ngulos de diferentes maneiras, porque eles sempre surgem como parte das decomposi&ccedil;&otilde;es.<\/p><p>As tr&ecirc;s formas principais s&atilde;o:<\/p><ul class=\"wp-block-list\">\n<li><strong>F&oacute;rmula base &times; altura: <\/strong>A = b&sdot;h\/2;<\/li>\n\n\n\n<li><strong>F&oacute;rmula trigonom&eacute;trica: <\/strong>A = a&sdot;b&sdot;sin&#8289;&theta;\/2&#8203;; e<\/li>\n\n\n\n<li><strong>F&oacute;rmula de Heron: <img decoding=\"async\" width=\"316\" height=\"22\" src=\"data:image\/png;base64,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\"><\/strong>.<\/li>\n<\/ul><h3 class=\"wp-block-heading\" id=\"h-areas-de-setores-circulares\">&Aacute;reas de setores circulares<\/h3><p>O setor circular aparece constantemente em tri&acirc;ngulos curvil&iacute;neos porque cada arco pertence a uma circunfer&ecirc;ncia, e a &aacute;rea &ldquo;recortada&rdquo; por esse arco nada mais &eacute; que um setor.<\/p><p>A f&oacute;rmula &eacute;:&nbsp;<\/p><ul class=\"wp-block-list\">\n<li>Em graus: A<sub>setor<\/sub> = (&theta;\/360) &sdot; &pi;r<sup>2<\/sup>; ou<\/li>\n\n\n\n<li>Em radianos: A<sub>setor<\/sub> = r<sup>2<\/sup> &sdot; &theta;\/2.<\/li>\n<\/ul><h3 class=\"wp-block-heading\" id=\"h-areas-de-segmentos-circulares\">&Aacute;reas de segmentos circulares<\/h3><p>O segmento circular &eacute; uma das pe&ccedil;as-chave para compor ou remover partes em um tri&acirc;ngulo curvil&iacute;neo. Ele &eacute; formado pelo <strong>arco<\/strong> e pela <strong>corda<\/strong> que une as extremidades do arco.<\/p><p>Para calcular sua &aacute;rea: A<sub>segmento<\/sub> = A<sub>setor<\/sub>&minus;A<sub>tri&acirc;ngulo associado<\/sub><\/p><h2 class=\"wp-block-heading\" id=\"h-exercicios-de-fixacao\"><span class=\"ez-toc-section\" id=\"Exercicios-de-fixacao\"><\/span>Exerc&iacute;cios de fixa&ccedil;&atilde;o<span class=\"ez-toc-section-end\"><\/span><\/h2><h3 class=\"wp-block-heading\" id=\"h-exercicio-1\">Exerc&iacute;cio 1<\/h3><p>Tr&ecirc;s circunfer&ecirc;ncias de raio 2 cm tangenciam-se externamente. Calcule a &aacute;rea do tri&acirc;ngulo curvil&iacute;neo central.<\/p><p>Resposta:<\/p><p>Acurvil&iacute;neo = <\/p><figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" width=\"382\" height=\"48\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/11\/image-1-59.png\" alt=\"\" class=\"wp-image-150461\" style=\"width:289px;height:auto\" srcset=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/11\/image-1-59.png 382w, https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/11\/image-1-59-380x48.png 380w\" sizes=\"(max-width: 382px) 100vw, 382px\" \/><\/figure><h3 class=\"wp-block-heading\" id=\"h-exercicio-2\">Exerc&iacute;cio 2<\/h3><p>Num tri&acirc;ngulo equil&aacute;tero de lado 8 cm, tra&ccedil;am-se arcos de circunfer&ecirc;ncia de raio 8 cm com centro nos v&eacute;rtices. Determine a &aacute;rea da regi&atilde;o central delimitada pelos arcos.<\/p><p><strong>Resposta:<\/strong><\/p><p>Acurvil&iacute;neo = Aequil&aacute;tero &ndash; Asetores<\/p><p>Acurvil&iacute;neo = <\/p><figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" width=\"329\" height=\"53\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/11\/image-1-60.png\" alt=\"\" class=\"wp-image-150462\" style=\"width:297px;height:auto\"><\/figure><h2 class=\"wp-block-heading\" id=\"h-erros-comuns-no-calculo-da-area-de-triangulos-curvilineos\"><span class=\"ez-toc-section\" id=\"Erros-comuns-no-calculo-da-area-de-triangulos-curvilineos\"><\/span>Erros comuns no c&aacute;lculo da &aacute;rea de tri&acirc;ngulos curvil&iacute;neos<span class=\"ez-toc-section-end\"><\/span><\/h2><ul class=\"wp-block-list\">\n<li>Confundir as &aacute;reas que devem ser somadas ou subtra&iacute;das. Uma estrat&eacute;gia &uacute;til &eacute; colorir as regi&otilde;es nos desenhos para visualizar o que sobra;<\/li>\n<\/ul><ul class=\"wp-block-list\">\n<li>Calcular incorretamente setores circulares. Lembre-se de que o &acirc;ngulo central deve ser convertido corretamente para graus ou radianos, dependendo da f&oacute;rmula.;<\/li>\n\n\n\n<li>Ignorar a dilata&ccedil;&atilde;o entre raio e lado do pol&iacute;gono. Muitas vezes, o raio dos arcos n&atilde;o coincide exatamente com o lado da figura; e<\/li>\n\n\n\n<li>Dificuldade em visualizar a decomposi&ccedil;&atilde;o. Um bom h&aacute;bito &eacute; sempre come&ccedil;ar desenhando a figura completa e destacando tri&acirc;ngulos, setores e segmentos antes de aplicar f&oacute;rmulas.<\/li>\n<\/ul><h2 class=\"wp-block-heading\" id=\"h-estude-com-o-estrategia-vestibulares\"><span class=\"ez-toc-section\" id=\"Estude-com-o-Estrategia-Vestibulares\"><\/span>Estude com o Estrat&eacute;gia Vestibulares<span class=\"ez-toc-section-end\"><\/span><\/h2><p>Aprenda matem&aacute;tica com os cursos do EV. Assim, voc&ecirc; ter&aacute; acesso aos melhores materiais para a sua prepara&ccedil;&atilde;o, como videoaulas e LDI, al&eacute;m de acesso ao banco de quest&otilde;es e ao f&oacute;rum de d&uacute;vidas para fazer perguntas diretamente aos professores. 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