{"id":10228,"date":"2012-10-12T01:48:51","date_gmt":"2012-10-12T00:48:51","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=10228"},"modified":"2022-01-20T22:53:49","modified_gmt":"2022-01-20T22:53:49","slug":"dois-quadrados-sobrepostos","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=10228","title":{"rendered":"Dois quadrados sobrepostos"},"content":{"rendered":"<p><ul id='GTTabs_ul_10228' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_10228' class='GTTabs_curr'><a  id=\"10228_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_10228' ><a  id=\"10228_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_10228'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Dois quadrados congruentes de $6$ cm de lado est\u00e3o sobrepostos como mostra a figura.<\/p>\n<p>O v\u00e9rtice de um dos quadrados est\u00e1 no centro do outro quadrado.<\/p>\n<p>Qual \u00e9 a \u00e1rea da parte sobreposta?<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/2quadradossobrepostos.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"10232\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=10232\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/2quadradossobrepostos.jpg\" data-orig-size=\"257,295\" 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;}\" data-image-title=\"Dois quadrados sobrepostos\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/2quadradossobrepostos.jpg\" class=\"wp-image-10232 aligncenter\" title=\"Dois quadrados sobrepostos\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/2quadradossobrepostos.jpg\" alt=\"\" width=\"123\" height=\"142\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/2quadradossobrepostos.jpg 257w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/2quadradossobrepostos-130x150.jpg 130w\" sizes=\"auto, (max-width: 123px) 100vw, 123px\" \/><\/a><\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_10228' onClick='GTTabs_show(1,10228)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_10228'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Explore a anima\u00e7\u00e3o seguinte:<\/p>\n<p style=\"text-align: center;\"><script src=\"https:\/\/cdn.geogebra.org\/apps\/deployggb.js\"><\/script>\r\n<div id=\"ggbApplet\" style=\"margin: 0 auto;\"><\/div>\r\n<script>\r\nvar parameters = {\r\n\"id\": \"ggbApplet\",\r\n\"width\":782,\r\n\"height\":429,\r\n\"showMenuBar\":false,\r\n\"showAlgebraInput\":false,\r\n\"showToolBar\":false,\r\n\"customToolBar\":\"0 39 59 || 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 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\"};\r\n\/\/ is3D=is 3D applet using 3D view, AV=Algebra View, SV=Spreadsheet View, CV=CAS View, EV2=Graphics View 2, CP=Construction Protocol, PC=Probability Calculator, DA=Data Analysis, FI=Function Inspector, PV=Python, macro=Macro View\r\nvar views = {'is3D': 0,'AV': 0,'SV': 0,'CV': 0,'EV2': 0,'CP': 0,'PC': 0,'DA': 0,'FI': 0,'PV': 0,'macro': 0};\r\nvar applet = new GGBApplet(parameters, '5.0', views);\r\nwindow.onload = function() {applet.inject('ggbApplet')};\r\n<\/script><\/p>\n<\/p>\n<p>Qual \u00e9 a justifica\u00e7\u00e3o para o resultado obtido?<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_10228' onClick='GTTabs_show(0,10228)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Dois quadrados congruentes de $6$ cm de lado est\u00e3o sobrepostos como mostra a figura. O v\u00e9rtice de um dos quadrados est\u00e1 no centro do outro quadrado. Qual \u00e9 a \u00e1rea da&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20790,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[321,97,322],"tags":[429,67,430],"series":[],"class_list":["post-10228","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-10-o-ano","category-aplicando","category-modulo-inicial","tag-10-o-ano","tag-geometria","tag-modulo-inicial"],"views":3645,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/10V1Pag039-30b_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/10228","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=10228"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/10228\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20790"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=10228"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=10228"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=10228"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=10228"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}