{"id":7379,"date":"2012-02-12T16:16:18","date_gmt":"2012-02-12T16:16:18","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7379"},"modified":"2022-01-16T21:31:54","modified_gmt":"2022-01-16T21:31:54","slug":"qual-e-o-poligono","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7379","title":{"rendered":"Qual \u00e9 o pol\u00edgono?"},"content":{"rendered":"<p><ul id='GTTabs_ul_7379' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7379' class='GTTabs_curr'><a  id=\"7379_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7379' ><a  id=\"7379_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_7379'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Qual \u00e9 o pol\u00edgono convexo cuja soma das amplitudes dos \u00e2ngulos internos \u00e9:<\/p>\n<ol>\n<li>720\u00ba<\/li>\n<li>1980\u00ba<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7379' onClick='GTTabs_show(1,7379)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7379'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>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>Tendo em considera\u00e7\u00e3o a rela\u00e7\u00e3o acima, temos: $$\\begin{array}{*{20}{l}} \u00a0 {(n &#8211; 2) \\times 180 = 720}&amp; \\Leftrightarrow &amp;{180n &#8211; 360 = 720} \\\\ \u00a0 {}&amp; \\Leftrightarrow &amp;{180n = 1080} \\\\ \u00a0 {}&amp; \\Leftrightarrow &amp;{n = 6} \\end{array}$$ Trata-se, portanto, de um hex\u00e1gono.<br \/>\n\u00ad<\/li>\n<li>Tendo em considera\u00e7\u00e3o a rela\u00e7\u00e3o acima, temos: $$\\begin{array}{*{20}{l}} \u00a0 {(n &#8211; 2) \\times 180 = 1980}&amp; \\Leftrightarrow &amp;{n &#8211; 2 = \\frac{{1980}}{{180}}} \\\\ \u00a0 {}&amp; \\Leftrightarrow &amp;{n &#8211; 2 = 11} \\\\ \u00a0 {}&amp; \\Leftrightarrow &amp;{n = 13} \\end{array}$$ Trata-se, portanto de um pol\u00edgono de 13 lados (tridec\u00e1gono).<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7379' onClick='GTTabs_show(0,7379)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Qual \u00e9 o pol\u00edgono convexo cuja soma das amplitudes dos \u00e2ngulos internos \u00e9: 720\u00ba 1980\u00ba Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20417,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,278],"tags":[426,281],"series":[],"class_list":["post-7379","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"],"views":1272,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/02\/9V1Pag031-2_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7379","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=7379"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7379\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20417"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7379"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7379"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7379"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7379"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}