{"id":11399,"date":"2012-11-15T22:09:45","date_gmt":"2012-11-15T22:09:45","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=11399"},"modified":"2022-01-20T14:29:29","modified_gmt":"2022-01-20T14:29:29","slug":"um-quadrado","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=11399","title":{"rendered":"Um quadrado"},"content":{"rendered":"<p><ul id='GTTabs_ul_11399' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_11399' class='GTTabs_curr'><a  id=\"11399_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_11399' ><a  id=\"11399_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_11399'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/quadrado2.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"11402\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=11402\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/quadrado2.jpg\" data-orig-size=\"245,238\" 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=\"Quadrado\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/quadrado2.jpg\" class=\"alignright wp-image-11402 size-full\" title=\"Quadrado\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/quadrado2.jpg\" alt=\"\" width=\"245\" height=\"238\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/quadrado2.jpg 245w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/quadrado2-150x145.jpg 150w\" sizes=\"auto, (max-width: 245px) 100vw, 245px\" \/><\/a>O comprimento do lado do quadrado [ABCD] \u00e9 $12$ cm.<\/p>\n<ol>\n<li>\u00a0Qual a \u00e1rea da parte sombreada?<\/li>\n<li>Existe um quadrado com a \u00e1rea da parte sombreada cujo comprimento do lado seja um n\u00famero natural? Se sim, indica o comprimento do seu lado.<\/li>\n<li>Se o comprimento do lado do quadrado [ABCD] fosse outro n\u00famero natural qualquer, chegavas \u00e0s mesmas conclus\u00f5es da al\u00ednea anterior? Explica a tua resposta.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_11399' onClick='GTTabs_show(1,11399)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_11399'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/quadrado2.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"11402\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=11402\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/quadrado2.jpg\" data-orig-size=\"245,238\" 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=\"Quadrado\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/quadrado2.jpg\" class=\"alignright wp-image-11402 size-full\" title=\"Quadrado\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/quadrado2.jpg\" alt=\"\" width=\"245\" height=\"238\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/quadrado2.jpg 245w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/quadrado2-150x145.jpg 150w\" sizes=\"auto, (max-width: 245px) 100vw, 245px\" \/><\/a>As diagonais de um quadrado dividem-no em quatro tri\u00e2ngulos geometricamente iguais.\n<p>Logo, a \u00e1rea sombreada \u00e9 um quarto da \u00e1rea do quadrado [ABCD].<\/p>\n<p>Como a \u00e1rea do quadrado [ABCD] \u00e9 ${A_{\\left[ {ABCD} \\right]}} = {12^2} = 144$ cm<sup>2<\/sup>, ent\u00e3o \u00e9 de $36$ cm<sup>2<\/sup> a \u00e1rea sombreada.<br \/>\n\u00ad<\/p>\n<\/li>\n<li>Sim, h\u00e1 um quadrado com a \u00e1rea da parte sombreada cujo comprimento do lado \u00e9 um n\u00famero natural: o quadrado com $6$ cm de comprimento do lado.<br \/>\n\u00ad<\/li>\n<li>Depende do n\u00famero natural que represente o comprimento do lado do quadrado [ABCD]. Obt\u00e9m-se a mesma conclus\u00e3o, quando esse n\u00famero natural \u00e9 tal que a quarta parte do seu quadrado \u00e9 um quadrado perfeito.\n<p>Esta conclus\u00e3o \u00e9 v\u00e1lida quando a medida do comprimento do lado do quadrado [ABCD] \u00e9 um n\u00famero natural par:<\/p>\n<\/li>\n<\/ol>\n<table class=\" aligncenter\" style=\"width: 80%;\" border=\"0\" align=\"center\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\">Comprimento do lado do<br \/>\nquadrado menor<\/td>\n<td style=\"text-align: center;\">\u00a0Quarta parte da \u00e1rea do<br \/>\nquadrado [ABCD]<\/td>\n<td style=\"text-align: center;\">\u00c1rea do quadrado<br \/>\n[ABCD]<\/td>\n<td style=\"text-align: center;\">Comprimento do\u00a0 lado do<br \/>\nquadrado [ABCD]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">\u00a0$1$<\/td>\n<td style=\"text-align: center;\">\u00a0$1$<\/td>\n<td style=\"text-align: center;\">\u00a0$4$<\/td>\n<td style=\"text-align: center;\">\u00a0$2$<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">\u00a0$2$<\/td>\n<td style=\"text-align: center;\">\u00a0$4$<\/td>\n<td style=\"text-align: center;\">\u00a0$16$<\/td>\n<td style=\"text-align: center;\">\u00a0$4$<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">\u00a0$3$<\/td>\n<td style=\"text-align: center;\">$9$<\/td>\n<td style=\"text-align: center;\">$36$<\/td>\n<td style=\"text-align: center;\">$6$<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">\u00a0$4$<\/td>\n<td style=\"text-align: center;\">$16$<\/td>\n<td style=\"text-align: center;\">$64$<\/td>\n<td style=\"text-align: center;\">$8$<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">\u00a0$5$<\/td>\n<td style=\"text-align: center;\">$25$<\/td>\n<td style=\"text-align: center;\">$100$<\/td>\n<td style=\"text-align: center;\">$10$<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">\u00a0$6$<\/td>\n<td style=\"text-align: center;\">$36$<\/td>\n<td style=\"text-align: center;\">$144$<\/td>\n<td style=\"text-align: center;\">$12$<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">\u00a0&#8230;<\/td>\n<td style=\"text-align: center;\">\u00a0&#8230;<\/td>\n<td style=\"text-align: center;\">\u00a0&#8230;<\/td>\n<td style=\"text-align: center;\">\u00a0&#8230;<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_11399' onClick='GTTabs_show(0,11399)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado O comprimento do lado do quadrado [ABCD] \u00e9 $12$ cm. \u00a0Qual a \u00e1rea da parte sombreada? Existe um quadrado com a \u00e1rea da parte sombreada cujo comprimento do lado seja um&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20742,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[317,97,318],"tags":[108,339],"series":[],"class_list":["post-11399","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-7-o-ano","category-aplicando","category-numeros-inteiros","tag-area","tag-raiz-quadrada"],"views":3649,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/7V1Pag039-10_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11399","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=11399"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11399\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20742"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=11399"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=11399"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=11399"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=11399"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}