{"id":14518,"date":"2018-04-14T23:18:19","date_gmt":"2018-04-14T22:18:19","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14518"},"modified":"2022-01-07T22:16:23","modified_gmt":"2022-01-07T22:16:23","slug":"um-quadrado-abcd","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14518","title":{"rendered":"Um quadrado [ABCD]"},"content":{"rendered":"<p><ul id='GTTabs_ul_14518' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14518' class='GTTabs_curr'><a  id=\"14518_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14518' ><a  id=\"14518_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_14518'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag92-1.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14519\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14519\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag92-1.png\" data-orig-size=\"275,283\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Quadrado\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag92-1.png\" class=\"alignright size-full wp-image-14519\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag92-1.png\" alt=\"\" width=\"275\" height=\"283\" \/><\/a>Na figura, est\u00e1 representado um quadrado [<em>ABCD<\/em>].<br \/>\nSabe-se que:<\/p>\n<ul>\n<li>o comprimento do lado do quadrado \u00e9 10.<\/li>\n<li><em>E<\/em>, <em>F<\/em>, <em>G<\/em> e <em>H<\/em> s\u00e3o os pontos m\u00e9dios dos lados [<em>AB<\/em>], [<em>BC<\/em>], [<em>CD<\/em>] e [<em>DA<\/em>], respetivamente.<\/li>\n<\/ul>\n<ol>\n<li>Qual \u00e9 a medida de [<em>EF<\/em>]?<br \/>\nApresenta os c\u00e1lculos que efetuaste.<br \/>\nEscreve o resultado arredondado \u00e0s d\u00e9cimas.<\/li>\n<li>Qual \u00e9 a \u00e1rea da regi\u00e3o sombreada [<em>AEFCGH<\/em>]?<br \/>\nEscreve a letra que apresenta a resposta correta.<br \/>\n[A] 100<br \/>\n[B] 75<br \/>\n[C] 50<br \/>\n[D] 45<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14518' onClick='GTTabs_show(1,14518)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14518'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag92-1.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14519\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14519\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag92-1.png\" data-orig-size=\"275,283\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Quadrado\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag92-1.png\" class=\"alignright size-full wp-image-14519\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag92-1.png\" alt=\"\" width=\"275\" height=\"283\" \/><\/a>Na figura, est\u00e1 representado um quadrado [<em>ABCD<\/em>].<br \/>\nSabe-se que:<\/p>\n<\/blockquote>\n<ul>\n<li>\n<blockquote>\n<p>o comprimento do lado do quadrado \u00e9 10.<\/p>\n<\/blockquote>\n<\/li>\n<li>\n<blockquote>\n<p><em>E<\/em>, <em>F<\/em>, <em>G<\/em> e <em>H<\/em> s\u00e3o os pontos m\u00e9dios dos lados [<em>AB<\/em>], [<em>BC<\/em>], [<em>CD<\/em>] e [<em>DA<\/em>], respetivamente.<\/p>\n<\/blockquote>\n<\/li>\n<\/ul>\n<p>\u00ad<\/p>\n<ol>\n<li>Aplicando o Teorema de Pit\u00e1goras no tri\u00e2ngulo ret\u00e2ngulo [<em>EBF<\/em>], vem:<br \/>\n\\[\\overline {EF} = \\sqrt {{{\\overline {EB} }^2} + {{\\overline {BF} }^2}} = \\sqrt {{5^2} + {5^2}} = 5\\sqrt 2 \\approx 7,1\\]<\/li>\n<li>A \u00e1rea da regi\u00e3o sombreada [<em>AEFCGH<\/em>] \u00e9 \\({A_S} = {A_{\\left[ {ABCD} \\right]}} &#8211; 2 \\times {A_{\\left[ {EBF} \\right]}} = 10 \\times 10 &#8211; 2 \\times \\frac{{5 \\times 5}}{2} = 75\\).<br \/>\nLogo, a alternativa correta \u00e9 a [A].<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14518' onClick='GTTabs_show(0,14518)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Na figura, est\u00e1 representado um quadrado [ABCD]. Sabe-se que: o comprimento do lado do quadrado \u00e9 10. E, F, G e H s\u00e3o os pontos m\u00e9dios dos lados [AB], [BC], [CD]&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14520,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,303],"tags":[426,108,118],"series":[],"class_list":["post-14518","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-equacoes-do-2-o-grau","tag-9-o-ano","tag-area","tag-teorema-de-pitagoras"],"views":2074,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag92-1a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14518","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=14518"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14518\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14520"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14518"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14518"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14518"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14518"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}