{"id":7383,"date":"2012-02-12T18:13:41","date_gmt":"2012-02-12T18:13:41","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7383"},"modified":"2022-01-06T00:31:02","modified_gmt":"2022-01-06T00:31:02","slug":"um-poligono-regular","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7383","title":{"rendered":"Um pol\u00edgono regular"},"content":{"rendered":"<p><ul id='GTTabs_ul_7383' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7383' class='GTTabs_curr'><a  id=\"7383_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7383' ><a  id=\"7383_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_7383'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Determina quantos lados tem um pol\u00edgono regular cujo \u00e2ngulo interno mede:<\/p>\n<ol>\n<li>140\u00ba<\/li>\n<li>135\u00ba<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7383' onClick='GTTabs_show(1,7383)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7383'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p style=\"text-align: center;\">A soma das amplitudes dos \u00e2ngulos internos de um pol\u00edgono convexo de $n$ lados \u00e9 dada por $$(n &#8211; 2) \\times 180^\\circ $$<\/p>\n<\/blockquote>\n<ol>\n<li>Como o pol\u00edgono \u00e9 regular, as amplitudes dos $n$ \u00e2ngulos internos \u00e9 igual.<br \/>\nLogo, considerando a rela\u00e7\u00e3o acima, temos:<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{\\frac{{(n &#8211; 2) \\times 180}}{n} = 140}&amp; \\Leftrightarrow &amp;{(n &#8211; 2) \\times 180 = 140n} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{180n &#8211; 360 = 140n} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{40n = 360} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{n = 9}<br \/>\n\\end{array}$$<br \/>\nPortanto, o pol\u00edgono regular considerado tem 9 lados.<br \/>\n\u00ad<\/li>\n<li>Como o pol\u00edgono \u00e9 regular, as amplitudes dos $n$ \u00e2ngulos internos \u00e9 igual.<br \/>\nLogo, considerando a rela\u00e7\u00e3o acima, temos:<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{\\frac{{(n &#8211; 2) \\times 180}}{n} = 135}&amp; \\Leftrightarrow &amp;{(n &#8211; 2) \\times 180 = 135n} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{180n &#8211; 360 = 135n} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{45n = 360} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{n = 8}<br \/>\n\\end{array}$$<br \/>\nPortanto, o pol\u00edgono regular considerado tem 8 lados.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7383' onClick='GTTabs_show(0,7383)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Determina quantos lados tem um pol\u00edgono regular cujo \u00e2ngulo interno mede: 140\u00ba 135\u00ba Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":14083,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,278],"tags":[426,283],"series":[],"class_list":["post-7383","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-circunferencia-e-poligonos","tag-9-o-ano","tag-poligono-regular"],"views":5470,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat28.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7383","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=7383"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7383\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7383"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7383"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7383"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7383"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}