{"id":14379,"date":"2018-04-11T09:32:26","date_gmt":"2018-04-11T08:32:26","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14379"},"modified":"2022-01-06T22:52:37","modified_gmt":"2022-01-06T22:52:37","slug":"areas-e-perimetros-1","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14379","title":{"rendered":"\u00c1reas e per\u00edmetros 1"},"content":{"rendered":"<p><ul id='GTTabs_ul_14379' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14379' class='GTTabs_curr'><a  id=\"14379_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14379' ><a  id=\"14379_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_14379'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag78-1-1.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14380\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14380\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag78-1-1.png\" data-orig-size=\"232,203\" 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=\"Trap\u00e9zio\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag78-1-1.png\" class=\"alignright wp-image-14380\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag78-1-1.png\" alt=\"\" width=\"200\" height=\"175\" \/><\/a>Observa o trap\u00e9zio ret\u00e2ngulo da figura.<\/p>\n<ol>\n<li>Determina a \u00e1rea do trap\u00e9zio, sabendo que\u00a0\\(x = 3\\) cm.<\/li>\n<li>Escreve uma express\u00e3o simplificada, na vari\u00e1vel <em>x<\/em>, que represente a \u00e1rea do trap\u00e9zio. Apresenta os c\u00e1lculos que efetuaste.<\/li>\n<li>Qual deve ser o valor de <em>x<\/em> para que a \u00e1rea do trap\u00e9zio seja igual a 54 cm<sup>2<\/sup>?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14379' onClick='GTTabs_show(1,14379)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14379'>\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\/2018\/04\/9V2Pag78-1-1.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14380\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14380\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag78-1-1.png\" data-orig-size=\"232,203\" 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=\"Trap\u00e9zio\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag78-1-1.png\" class=\"alignright wp-image-14380\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag78-1-1.png\" alt=\"\" width=\"200\" height=\"175\" \/><\/a>Se \\(x = 3\\) cm, o trap\u00e9zio tem 33 cm<sup>2<\/sup> de \u00e1rea:<br \/>\n\\[A\\left( 3 \\right) = \\frac{{\\overline {AB} + \\overline {CD} }}{2} \\times \\overline {AD} = \\frac{{15 + 7}}{2} \\times 3 = 33\\]<\/li>\n<li>A express\u00e3o seguinte, na vari\u00e1vel <em>x<\/em>, representa a \u00e1rea do trap\u00e9zio:<br \/>\n\\[A\\left( x \\right) = \\frac{{\\overline {AB} + \\overline {CD} }}{2} \\times \\overline {AD} = \\frac{{5x + \\left( {2x + 1} \\right)}}{2} \\times 3 = \\frac{{21x + 3}}{2}\\]<\/li>\n<li>Para a \u00e1rea do trap\u00e9zio ser igual a 54 cm<sup>2<\/sup>, o valor de <em>x<\/em> \u00e9 5:<br \/>\n\\[\\begin{array}{*{20}{l}}{A\\left( x \\right) = 54}&amp; \\Leftrightarrow &amp;{\\frac{{21x + 3}}{2} = 54}\\\\{}&amp; \\Leftrightarrow &amp;{21x + 3 = 108}\\\\{}&amp; \\Leftrightarrow &amp;{x = \\frac{{105}}{{21}}}\\\\{}&amp; \\Leftrightarrow &amp;{x = 5}\\end{array}\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14379' onClick='GTTabs_show(0,14379)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Observa o trap\u00e9zio ret\u00e2ngulo da figura. Determina a \u00e1rea do trap\u00e9zio, sabendo que\u00a0\\(x = 3\\) cm. Escreve uma express\u00e3o simplificada, na vari\u00e1vel x, que represente a \u00e1rea do trap\u00e9zio. Apresenta os&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14381,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,303],"tags":[426,306],"series":[],"class_list":["post-14379","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-equacao-do-2-o-grau"],"views":1428,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag78-1-1a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14379","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=14379"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14379\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14381"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14379"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14379"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14379"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14379"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}