{"id":23673,"date":"2022-12-10T22:38:32","date_gmt":"2022-12-10T22:38:32","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=23673"},"modified":"2022-12-28T00:01:42","modified_gmt":"2022-12-28T00:01:42","slug":"considera-a-figura-ao-lado","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=23673","title":{"rendered":"Considera a figura ao lado"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_23673' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_23673' class='GTTabs_curr'><a  id=\"23673_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_23673' ><a  id=\"23673_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_23673'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-2.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23675\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23675\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-2.png\" data-orig-size=\"413,260\" 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=\"8_Pag070-2\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-2.png\" class=\"alignright wp-image-23675\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-2-300x189.png\" alt=\"\" width=\"300\" height=\"189\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-2-300x189.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-2.png 413w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Considera a figura ao lado, onde:<\/p>\n<ul style=\"list-style-type: disc;\">\n<li>G \u00e9 um ponto do segmento de reta [BF];<\/li>\n<li>[ABGH] \u00e9 um quadrado;<\/li>\n<li>[BCEF] \u00e9 um quadrado;<\/li>\n<li>\\(\\overline {AH} = 6\\) e \\(\\overline {FG} = 2\\).<\/li>\n<\/ul>\n<ol>\n<li>Qual \u00e9 o comprimento da diagonal do quadrado [ABGH]?<br \/>Apresenta todos os c\u00e1lculos que efetuares e indica o resultado arredondado \u00e0s d\u00e9cimas.<\/li>\n<li>Determina a \u00e1rea do quadril\u00e1tero [ACDG], sombreado na figura.<br \/>Apresenta todos os c\u00e1lculos que efetuares.<\/li>\n<li>Como se designa o quadril\u00e1tero [ACDG]?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_23673' onClick='GTTabs_show(1,23673)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_23673'>\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\/2022\/12\/8_Pag070-2.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23675\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23675\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-2.png\" data-orig-size=\"413,260\" 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=\"8_Pag070-2\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-2.png\" class=\"alignright wp-image-23675\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-2-300x189.png\" alt=\"\" width=\"300\" height=\"189\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-2-300x189.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-2.png 413w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Considera a figura ao lado, onde:<\/p>\n<\/blockquote>\n<ul style=\"list-style-type: disc;\">\n<li>\n<blockquote>G \u00e9 um ponto do segmento de reta [BF];<\/blockquote>\n<\/li>\n<li>\n<blockquote>[ABGH] \u00e9 um quadrado;<\/blockquote>\n<\/li>\n<li>\n<blockquote>[BCEF] \u00e9 um quadrado;<\/blockquote>\n<\/li>\n<li>\n<blockquote>\\(\\overline {AH} = 6\\) e \\(\\overline {FG} = 2\\).<\/blockquote>\n<\/li>\n<\/ul>\n<ol>\n<li>\n<blockquote>Qual \u00e9 o comprimento da diagonal do quadrado [ABGH]?<br \/>Apresenta todos os c\u00e1lculos que efetuares e indica o resultado arredondado \u00e0s d\u00e9cimas.<\/blockquote>\n<\/li>\n<li>\n<blockquote>Determina a \u00e1rea do quadril\u00e1tero [ACDG], sombreado na figura.<br \/>Apresenta todos os c\u00e1lculos que efetuares.<\/blockquote>\n<\/li>\n<li>\n<blockquote>Como se designa o quadril\u00e1tero [ACDG]?<\/blockquote>\n<\/li>\n<\/ol>\n<p>\u00a0<\/p>\n<ol>\n<li>Aplicando o Teorema de Pit\u00e1goras no Tri\u00e2ngulo ret\u00e2ngulo [ABG], vem:<br \/>\\[\\overline {AG} = \\sqrt {{{\\overline {AB} }^2} + {{\\overline {BG} }^2}} = \\sqrt {{6^2} + {6^2}} = \\sqrt {36 \\times 2} = \\sqrt {36} \\times \\sqrt 2 = 6\\sqrt 2 \\]<br \/>Portanto, o comprimento da diagonal do quadrado [ABGH] \u00e9 \\(\\overline {AG} = 6\\sqrt 2 \\approx 8,5\\) u.c.<br \/><br \/><\/li>\n<li>\\[{A_{\\left[ {ACDG} \\right]}} = \\frac{{\\overline {AC} + \\overline {DG} }}{2} \\times \\overline {BG} = \\frac{{14 + 8}}{2} \\times 6 = 11 \\times 6 = 66\\]<br \/>O quadril\u00e1tero [ACDG] tem de \u00e1rea 66 u.a.<br \/><br \/><\/li>\n<li>O quadril\u00e1tero [ACDG] designa-se trap\u00e9zio ret\u00e2ngulo.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_23673' onClick='GTTabs_show(0,23673)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considera a figura ao lado, onde: G \u00e9 um ponto do segmento de reta [BF]; [ABGH] \u00e9 um quadrado; [BCEF] \u00e9 um quadrado; \\(\\overline {AH} = 6\\) e \\(\\overline {FG} =&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":23676,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,682],"tags":[424,108,67,118],"series":[],"class_list":["post-23673","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-teorema-de-pitagoras","tag-8-o-ano","tag-area","tag-geometria","tag-teorema-de-pitagoras"],"views":229,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-2_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23673","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=23673"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23673\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/23676"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=23673"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=23673"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=23673"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=23673"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}