{"id":14832,"date":"2018-04-24T00:13:02","date_gmt":"2018-04-23T23:13:02","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14832"},"modified":"2022-01-10T00:24:08","modified_gmt":"2022-01-10T00:24:08","slug":"partes-dos-graficos-de-duas-funcoes-e-um-trapezio-retangulo","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14832","title":{"rendered":"Partes dos gr\u00e1ficos de duas fun\u00e7\u00f5es e um trap\u00e9zio ret\u00e2ngulo"},"content":{"rendered":"<p><ul id='GTTabs_ul_14832' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14832' class='GTTabs_curr'><a  id=\"14832_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14832' ><a  id=\"14832_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_14832'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag123-10.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14833\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14833\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag123-10.png\" data-orig-size=\"564,446\" 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=\"Gr\u00e1ficos\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag123-10.png\" class=\"alignright wp-image-14833\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag123-10-300x237.png\" alt=\"\" width=\"400\" height=\"316\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag123-10-300x237.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag123-10.png 564w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/a>Na figura, est\u00e3o representadas, num referencial cartesiano de origem <em>O<\/em>, partes dos gr\u00e1ficos de duas fun\u00e7\u00f5es, <em>f<\/em> e <em>g<\/em>, bem como o trap\u00e9zio ret\u00e2ngulo [ABCD].<br \/>\nSabe-se que:<\/p>\n<ul>\n<li>os pontos <em>A<\/em> e <em>D<\/em> pertencem ao eixo das ordenadas;<\/li>\n<li>a fun\u00e7\u00e3o <em>f<\/em> \u00e9 definida por \\(f\\left( x \\right) = \\frac{1}{2}x\\);<\/li>\n<li>a fun\u00e7\u00e3o <em>g<\/em> \u00e9 definida por \\(g\\left( x \\right) = 2{x^2}\\);<\/li>\n<li>o ponto <em>B<\/em> pertence ao gr\u00e1fico da fun\u00e7\u00e3o <em>g<\/em> e tem abcissa 2;<\/li>\n<li>o ponto <em>C<\/em> pertence ao gr\u00e1fico da fun\u00e7\u00e3o <em>f<\/em> e tem abcissa 4.<\/li>\n<\/ul>\n<ol>\n<li>Identifica, usando letras da figura, dois pontos com a mesma ordenada.<\/li>\n<li>Determina a \u00e1rea do trap\u00e9zio [<em>ABCD<\/em>].<br \/>\nMostra como chegaste \u00e0 tua resposta.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14832' onClick='GTTabs_show(1,14832)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14832'>\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\/9V2Pag123-10.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14833\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14833\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag123-10.png\" data-orig-size=\"564,446\" 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=\"Gr\u00e1ficos\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag123-10.png\" class=\"alignright wp-image-14833\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag123-10-300x237.png\" alt=\"\" width=\"400\" height=\"316\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag123-10-300x237.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag123-10.png 564w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/a>Na figura, est\u00e3o representadas, num referencial cartesiano de origem <em>O<\/em>, partes dos gr\u00e1ficos de duas fun\u00e7\u00f5es, <em>f<\/em> e <em>g<\/em>, bem como o trap\u00e9zio ret\u00e2ngulo [ABCD].<br \/>\nSabe-se que:<\/p>\n<\/blockquote>\n<ul>\n<li>\n<blockquote>\n<p>os pontos <em>A<\/em> e <em>D<\/em> pertencem ao eixo das ordenadas;<\/p>\n<\/blockquote>\n<\/li>\n<li>\n<blockquote>\n<p>a fun\u00e7\u00e3o <em>f<\/em> \u00e9 definida por \\(f\\left( x \\right) = \\frac{1}{2}x\\);<\/p>\n<\/blockquote>\n<\/li>\n<li>\n<blockquote>\n<p>a fun\u00e7\u00e3o <em>g<\/em> \u00e9 definida por \\(g\\left( x \\right) = 2{x^2}\\);<\/p>\n<\/blockquote>\n<\/li>\n<li>\n<blockquote>\n<p>o ponto <em>B<\/em> pertence ao gr\u00e1fico da fun\u00e7\u00e3o <em>g<\/em> e tem abcissa 2;<\/p>\n<\/blockquote>\n<\/li>\n<li>\n<blockquote>\n<p>o ponto <em>C<\/em> pertence ao gr\u00e1fico da fun\u00e7\u00e3o <em>f<\/em> e tem abcissa 4.<\/p>\n<\/blockquote>\n<p>\u00ad<\/p>\n<\/li>\n<\/ul>\n<ol>\n<li>Dois pontos com a mesma ordenada s\u00e3o, por exemplo, os pontos A e B.<br \/>\n\u00ad<\/li>\n<li>Comecemos por determinar a altura do trap\u00e9zio:\\[\\overline {AD} = g\\left( 2 \\right) &#8211; f\\left( 4 \\right) = 2 \\times {2^2} &#8211; \\frac{1}{2} \\times 4 = 8 &#8211; 2 = 6\\]Logo, tem-se para a \u00e1rea do trap\u00e9zio:\\[{A_{\\left[ {ABCD} \\right]}} = \\frac{{\\overline {CD} + \\overline {AB} }}{2} \\times \\overline {AD} = \\frac{{4 + 2}}{2} \\times 6 = 18\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14832' onClick='GTTabs_show(0,14832)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Na figura, est\u00e3o representadas, num referencial cartesiano de origem O, partes dos gr\u00e1ficos de duas fun\u00e7\u00f5es, f e g, bem como o trap\u00e9zio ret\u00e2ngulo [ABCD]. Sabe-se que: os pontos A e&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14834,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,249],"tags":[426,345,499,500],"series":[],"class_list":["post-14832","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-proporcionalidade-inversa-e-funcoes-algebricas","tag-9-o-ano","tag-funcao-afim","tag-funcao-quadratica","tag-parabola"],"views":4601,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag123-10a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14832","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=14832"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14832\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14834"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14832"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14832"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14832"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14832"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}