{"id":2189,"date":"2026-10-15T01:36:58","date_gmt":"2026-10-15T00:36:58","guid":{"rendered":"https:\/\/wpcalc.com\/pt\/matematica\/area-de-poligono-regular\/"},"modified":"2026-10-15T01:36:58","modified_gmt":"2026-10-15T00:36:58","slug":"area-de-poligono-regular","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/pt\/matematica\/area-de-poligono-regular\/","title":{"rendered":"Calculadora de \u00e1rea de pol\u00edgono regular"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Calcule a \u00e1rea de um pol\u00edgono regular<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"2189\" data-favorite-title=\"\u00c1rea de pol\u00edgono regular\" data-favorite-url=\"https:\/\/wpcalc.com\/pt\/matematica\/area-de-poligono-regular\/\" data-favorite-excerpt=\"Calcule a \u00e1rea de qualquer pol\u00edgono regular a partir do comprimento do lado, da apotema ou do circunraio. Informe o n\u00famero de lados e uma dimens\u00e3o conhecida para obter a \u00e1rea, o per\u00edmetro e os \u00e2ngulos.\" aria-label=\"Adicionar aos favoritos\" data-favorite-icon=\"icon icon-geometry\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/pt\/matematica\/area-de-poligono-regular\/\" method=\"POST\" class=\"calculator\" id=\"calculator-2189\" data-post=\"2189\"><fieldset class=\"fieldset-input is-2\"><legend class=\"sr-only\">Campos de entrada<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">N\u00famero de lados (n)<\/label><div class=\"term\">n<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"nmero_de_lados_n\" id=\"field-1\" aria-describedby=\"calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"6\" min=\"3\" max=\"10000\" value=\"6\"\/><small id=\"calc-info-1\">N\u00famero inteiro de lados iguais, 3 ou mais.<\/small><\/div><div class=\"field\" id=\"input-2\"><label for=\"field-2\">Grandeza conhecida<\/label><div class=\"grid grid-cols-1\"><select id=\"field-2\" name=\"grandeza_conhecida\"><option value=\"side\" selected>Comprimento do lado (s)<\/option><option value=\"apothem\">Ap\u00f3tema (a)<\/option><option value=\"circumradius\">Circunraio (R)<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">Comprimento do lado (s)<\/label><div class=\"term\">s<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"comprimento_do_lado_s\" id=\"field-3\" aria-describedby=\"calc-info-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"10\" min=\"0\" value=\"10\"\/><div class=\"grid grid-cols-1\"><select id=\"field-4\" name=\"unidade\" aria-label=\"Unidade\"><option value=\"m\">m<\/option><option value=\"cm\" selected>cm<\/option><option value=\"mm\">mm<\/option><option value=\"ft\">ft<\/option><option value=\"in\">in<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-3\">Comprimento de um lado do pol\u00edgono.<\/small><\/div><div class=\"field has-term\" id=\"input-4\" hidden><label for=\"field-5\">Ap\u00f3tema (a)<\/label><div class=\"term\">a<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"aptema_a\" id=\"field-5\" aria-describedby=\"calc-info-5\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"8.66\" min=\"0\" value=\"8.66\"\/><div class=\"grid grid-cols-1\"><select id=\"field-6\" name=\"unidade\" aria-label=\"Unidade\"><option value=\"m\">m<\/option><option value=\"cm\" selected>cm<\/option><option value=\"mm\">mm<\/option><option value=\"ft\">ft<\/option><option value=\"in\">in<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-5\">Dist\u00e2ncia do centro ao ponto m\u00e9dio de um lado (inraio).<\/small><\/div><div class=\"field has-term\" id=\"input-5\" hidden><label for=\"field-7\">Circunraio (R)<\/label><div class=\"term\">R<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"circunraio_r\" id=\"field-7\" aria-describedby=\"calc-info-7\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"10\" min=\"0\" value=\"10\"\/><div class=\"grid grid-cols-1\"><select id=\"field-8\" name=\"unidade\" aria-label=\"Unidade\"><option value=\"m\">m<\/option><option value=\"cm\" selected>cm<\/option><option value=\"mm\">mm<\/option><option value=\"ft\">ft<\/option><option value=\"in\">in<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-7\">Dist\u00e2ncia do centro a um v\u00e9rtice (raio da circunfer\u00eancia circunscrita).<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Recalcular\" id=\"calculate-button\" data-post=\"2189\">Calcular<\/button><button type=\"reset\">Redefinir<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calcular automaticamente<\/label><small>Se ativado, o resultado \u00e9 atualizado automaticamente quando voc\u00ea altera qualquer valor.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Seu pol\u00edgono<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>\u00c1rea<\/span><span class=\"result-term\">A<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-2\"><span class=\"field-title\"><span>Per\u00edmetro<\/span><span class=\"result-term\">P<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-3\"><span class=\"field-title\"><span>Comprimento do lado<\/span><span class=\"result-term\">s<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-4\"><span class=\"field-title\"><span>Ap\u00f3tema<\/span><span class=\"result-term\">a<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-5\"><span class=\"field-title\"><span>Circunraio<\/span><span class=\"result-term\">R<\/span><\/span><span class=\"field-value\" id=\"result-5\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-6\"><span class=\"field-title\"><span>\u00c2ngulo interno<\/span><span class=\"result-term\">\u03b1<\/span><\/span><span class=\"field-value\" id=\"result-6\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-7\"><span class=\"field-title\"><span>Etapas do c\u00e1lculo<\/span><\/span><span class=\"field-value\" id=\"result-7\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Copiar link para este c\u00e1lculo<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Deixar um coment\u00e1rio<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"2189\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">O que voc\u00ea achou deste resultado?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Curti <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">\u00datil <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Confuso <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Decepcionado <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Impreciso <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>\u00c1rea de pol\u00edgono regular<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">F\u00f3rmula<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ A = \\frac{n\\,s^2}{4\\tan(\\pi\/n)} = \\frac{1}{2}\\,P\\,a = \\frac{1}{2}\\,n\\,R^2\\sin\\!\\left(\\frac{2\\pi}{n}\\right) \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Onde:<\/strong><\/p>\n<ul>\n<li>\\(n\\) \u2014 n\u00famero de lados (\\(n \\ge 3\\))<\/li>\n<li>\\(s\\) \u2014 comprimento de um lado<\/li>\n<li>\\(a\\) \u2014 apotema (dist\u00e2ncia do centro ao ponto m\u00e9dio de um lado, ou seja, o raio da circunfer\u00eancia inscrita)<\/li>\n<li>\\(R\\) \u2014 circunraio (dist\u00e2ncia do centro a um v\u00e9rtice)<\/li>\n<li>\\(P = n \\cdot s\\) \u2014 per\u00edmetro<\/li>\n<li>\\(\\pi \\approx 3.14159\\)<\/li>\n<\/ul>\n<p>As tr\u00eas express\u00f5es d\u00e3o a mesma \u00e1rea; use a que corresponde \u00e0 dimens\u00e3o que voc\u00ea conhece. A forma central, \\(A = \\tfrac{1}{2}Pa\\), \u00e9 o resultado cl\u00e1ssico obtido ao dividir o pol\u00edgono em \\(n\\) tri\u00e2ngulos id\u00eanticos, cada um com base \\(s\\) e altura \\(a\\).<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-2\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>\u00c1rea de pol\u00edgono regular \u2013 Exemplo de c\u00e1lculo<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Exemplo:<\/strong> um hex\u00e1gono regular com lado de 10 cm.<\/p>\n<p>\\[ a = \\frac{s}{2\\tan(\\pi\/n)} = \\frac{10}{2\\tan(\\pi\/6)} = \\frac{10}{2 \\cdot 0.5774} \\approx 8.660 \\text{ cm} \\]<\/p>\n<p>\\[ P = n \\cdot s = 6 \\cdot 10 = 60 \\text{ cm} \\]<\/p>\n<p>\\[ A = \\tfrac{1}{2}\\,P\\,a = \\tfrac{1}{2} \\cdot 60 \\cdot 8.660 \\approx 259.81 \\text{ cm}^2 \\]<\/p>\n<p><strong>Resultado:<\/strong> a \u00e1rea \u00e9 de aproximadamente <strong>259,81 cm\u00b2<\/strong>. A calculadora tamb\u00e9m informa o circunraio \\(R = 10\\) cm e um \u00e2ngulo interno de 120\u00b0.<\/p>\n<p>\n\r\n<\/section>\n<h2>Como usar a calculadora<\/h2>\n<ol>\n<li>Informe o <strong>n\u00famero de lados (n)<\/strong> \u2014 qualquer n\u00famero inteiro de 3 (tri\u00e2ngulo) at\u00e9 10.000.<\/li>\n<li>Escolha a dimens\u00e3o que voc\u00ea conhece no menu <strong>Grandeza conhecida<\/strong>: <em>Comprimento do lado (s)<\/em>, <em>Apotema (a)<\/em> ou <em>Circunraio (R)<\/em>. Apenas o campo correspondente permanece vis\u00edvel.<\/li>\n<li>Digite o valor no campo que aparecer \u2014 <strong>Comprimento do lado (s)<\/strong>, <strong>Apotema (a)<\/strong> ou <strong>Circunraio (R)<\/strong> \u2014 e escolha a unidade (m, cm, mm, ft ou in).<\/li>\n<li>Leia os resultados: <strong>\u00c1rea<\/strong> (na unidade quadrada correspondente), al\u00e9m de <strong>Per\u00edmetro<\/strong>, <strong>Comprimento do lado<\/strong>, <strong>Apotema<\/strong>, <strong>Circunraio<\/strong>, <strong>\u00c2ngulo interno<\/strong> e uma dedu\u00e7\u00e3o passo a passo.<\/li>\n<\/ol>\n<h2>O que \u00e9 um pol\u00edgono regular?<\/h2>\n<p>Um pol\u00edgono regular \u00e9 uma figura fechada de lados retos em que todos os lados t\u00eam o mesmo comprimento e todos os \u00e2ngulos internos s\u00e3o iguais. Exemplos conhecidos s\u00e3o o tri\u00e2ngulo equil\u00e1tero (\\(n=3\\)), o quadrado (\\(n=4\\)), o pent\u00e1gono regular (\\(n=5\\)) e o hex\u00e1gono regular (\\(n=6\\)). Como todos os lados e \u00e2ngulos coincidem, um pol\u00edgono regular fica totalmente determinado por apenas dois n\u00fameros: o n\u00famero de lados e uma dimens\u00e3o linear.<\/p>\n<p>A f\u00f3rmula da \u00e1rea funciona fatiando o pol\u00edgono em \\(n\\) tri\u00e2ngulos congruentes que se encontram no centro. Cada tri\u00e2ngulo tem base \\(s\\) (um lado do pol\u00edgono) e altura \\(a\\) (a apotema), ent\u00e3o sua \u00e1rea \u00e9 \\(\\tfrac{1}{2}sa\\). Multiplicando pelos \\(n\\) lados, obt\u00e9m-se \\(A = \\tfrac{1}{2}nas = \\tfrac{1}{2}Pa\\). \u00c9 a mesma l\u00f3gica usada para chegar \u00e0 \u00e1rea do c\u00edrculo no limite: quando \\(n\\) fica muito grande, o pol\u00edgono torna-se indistingu\u00edvel de um c\u00edrculo de raio \\(R\\), e a f\u00f3rmula aproxima-se de \\(\\pi R^2\\).<\/p>\n<p>Duas dimens\u00f5es derivadas merecem aten\u00e7\u00e3o. A <strong>apotema<\/strong> \u00e9 o raio do c\u00edrculo inscrito \u2014 o maior c\u00edrculo que cabe dentro do pol\u00edgono, tangenciando cada lado no seu ponto m\u00e9dio. O <strong>circunraio<\/strong> \u00e9 o raio da circunfer\u00eancia circunscrita, que passa por todos os v\u00e9rtices. As tr\u00eas dimens\u00f5es est\u00e3o ligadas pelas identidades \\(s = 2a\\tan(\\pi\/n) = 2R\\sin(\\pi\/n)\\) e \\(a = R\\cos(\\pi\/n)\\) \u2014 por isso a calculadora consegue deduzir todas elas a partir de qualquer uma.<\/p>\n<p>O <strong>\u00e2ngulo interno<\/strong> exibido nos resultados vem de \\(\\alpha = (n-2) \\cdot 180\u00b0\/n\\). Ele \u00e9 \u00fatil na constru\u00e7\u00e3o civil, no assentamento de revestimentos e na marcenaria: por exemplo, um hex\u00e1gono tem cantos de 120\u00b0, ent\u00e3o voc\u00ea corta as pe\u00e7as a 60\u00b0 em meia esquadria para uni-las.<\/p>\n<h2>Premissas, limita\u00e7\u00f5es e dicas<\/h2>\n<ul>\n<li><strong>Apenas pol\u00edgonos regulares.<\/strong> As f\u00f3rmulas dependem de todos os lados e \u00e2ngulos serem iguais. Para um pol\u00edgono irregular, divida-o em tri\u00e2ngulos ou trap\u00e9zios e some as \u00e1reas.<\/li>\n<li><strong>Unidades devem ser coerentes.<\/strong> O seletor de unidades converte o valor digitado automaticamente, e a \u00e1rea \u00e9 devolvida na unidade quadrada correspondente (por exemplo, cm \u2192 cm\u00b2). Se voc\u00ea calcular \u00e0 m\u00e3o, mantenha todos os comprimentos na mesma unidade antes de aplicar a f\u00f3rmula.<\/li>\n<li><strong>Escolha a dimens\u00e3o que voc\u00ea realmente mediu.<\/strong> Na pr\u00e1tica, costuma-se conhecer a dist\u00e2ncia entre faces (o dobro da apotema, quando \\(n\\) \u00e9 par) ou o raio do c\u00edrculo de furos (circunraio), e n\u00e3o o lado \u2014 escolha essa op\u00e7\u00e3o para evitar erros de arredondamento numa convers\u00e3o intermedi\u00e1ria.<\/li>\n<li><strong>\\(n\\) grande.<\/strong> S\u00e3o aceitos valores at\u00e9 10.000; para figuras assim, o resultado \u00e9 praticamente a \u00e1rea de um c\u00edrculo de raio \\(R\\), j\u00e1 que \\(A \\to \\pi R^2\\) quando \\(n \\to \\infty\\).<\/li>\n<li><strong>Arredondamento.<\/strong> Os resultados s\u00e3o exibidos com tr\u00eas casas decimais. Os valores intermedi\u00e1rios nos passos do c\u00e1lculo s\u00e3o arredondados apenas para exibi\u00e7\u00e3o, ent\u00e3o uma confer\u00eancia manual pode diferir no \u00faltimo d\u00edgito.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Calcule a \u00e1rea de qualquer pol\u00edgono regular a partir do comprimento do lado, da apotema ou do circunraio. Informe o n\u00famero de lados e uma dimens\u00e3o conhecida para obter a \u00e1rea, o per\u00edmetro e os \u00e2ngulos.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[8],"tags":[42],"class_list":["post-2189","post","type-post","status-publish","format-standard","hentry","category-matematica","tag-geometria"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/posts\/2189","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/comments?post=2189"}],"version-history":[{"count":0,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/posts\/2189\/revisions"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/media?parent=2189"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/categories?post=2189"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/tags?post=2189"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}