{"id":5666,"date":"2010-11-19T00:45:50","date_gmt":"2010-11-19T00:45:50","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=5666"},"modified":"2022-01-19T17:40:49","modified_gmt":"2022-01-19T17:40:49","slug":"determina-as-areas","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=5666","title":{"rendered":"Determina as \u00e1reas"},"content":{"rendered":"<p><ul id='GTTabs_ul_5666' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_5666' class='GTTabs_curr'><a  id=\"5666_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_5666' ><a  id=\"5666_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_5666'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag23-5.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"5669\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=5669\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag23-5.jpg\" data-orig-size=\"347,227\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;HP pstc4380&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=\"pag23-5\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag23-5.jpg\" class=\"alignright wp-image-5669\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag23-5-300x196.jpg\" alt=\"\" width=\"300\" height=\"196\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag23-5-300x196.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag23-5-150x98.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag23-5.jpg 347w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Considerando a figura ao lado, determina a \u00e1rea:<\/p>\n<ol>\n<li>do ret\u00e2ngulo [ABCD];<\/li>\n<li>do tri\u00e2ngulo [BMC];<\/li>\n<li>do trap\u00e9zio [ABME].<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_5666' onClick='GTTabs_show(1,5666)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_5666'>\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\/2010\/11\/pag23-5.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"5669\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=5669\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag23-5.jpg\" data-orig-size=\"347,227\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;HP pstc4380&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=\"pag23-5\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag23-5.jpg\" class=\"alignright wp-image-5669\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag23-5-300x196.jpg\" alt=\"\" width=\"300\" height=\"196\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag23-5-300x196.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag23-5-150x98.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag23-5.jpg 347w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>A \u00e1rea do ret\u00e2ngulo [ABCD] \u00e9:\n<p>$$\\begin{array}{*{35}{l}}<br \/>\n{{A}_{[ABCD]}} &amp; = &amp; \\overline{AB}\\times \\overline{BC}\u00a0 \\\\<br \/>\n{} &amp; = &amp; 6\\times 4\u00a0 \\\\<br \/>\n{} &amp; = &amp; 24\\,\\,c{{m}^{2}}\u00a0 \\\\<br \/>\n\\end{array}$$<\/p>\n<\/li>\n<li>A \u00e1rea do tri\u00e2ngulo [BMC] \u00e9:\n<p>$$\\begin{array}{*{35}{l}}<br \/>\n{{A}_{[BMC]}} &amp; = &amp; \\frac{\\overline{BC}\\times \\overline{MF}}{2}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\frac{4\\times (6-4)}{2}\u00a0 \\\\<br \/>\n{} &amp; = &amp; 4\\,\\,c{{m}^{2}}\u00a0 \\\\<br \/>\n\\end{array}$$<\/p>\n<p><strong>Nota<\/strong>: O ponto F \u00e9 o ponto m\u00e9dio do segmento de reta [BC].<\/p>\n<\/li>\n<li>A \u00e1rea do trap\u00e9zio [ABME] \u00e9:\n<p>\\[\\begin{array}{*{35}{l}}<br \/>\n{{A}_{[ABME]}} &amp; = &amp; \\frac{{{A}_{[ABCD]}}-{{A}_{[BMC]}}}{2}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\frac{24-4}{2}\u00a0 \\\\<br \/>\n{} &amp; = &amp; 10\\,\\,c{{m}^{2}}\u00a0 \\\\<br \/>\n\\end{array}\\]<br \/>\n(Porqu\u00ea?)<\/p>\n<p><strong><br \/>\nALTERNATIVA<\/strong>:<\/p>\n<p>\\[\\begin{array}{*{35}{l}}<br \/>\n{{A}_{[ABME]}} &amp; = &amp; \\frac{\\overline{AB}+\\overline{EM}}{2}\\times \\overline{AE}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\frac{6+4}{2}\\times 2\u00a0 \\\\<br \/>\n{} &amp; = &amp; 10\\,\\,c{{m}^{2}}\u00a0 \\\\<br \/>\n\\end{array}\\]<br \/>\n(Usando a f\u00f3rmula da \u00e1rea do trap\u00e9zio)<\/p>\n<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_5666' onClick='GTTabs_show(0,5666)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considerando a figura ao lado, determina a \u00e1rea: do ret\u00e2ngulo [ABCD]; do tri\u00e2ngulo [BMC]; do trap\u00e9zio [ABME]. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20655,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,112],"tags":[424,108,67],"series":[],"class_list":["post-5666","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-decomposicao-de-figuras-teorema-de-pitagoras","tag-8-o-ano","tag-area","tag-geometria"],"views":2650,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/8V1Pag023-5_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/5666","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=5666"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/5666\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20655"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5666"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5666"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5666"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=5666"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}