{"id":23639,"date":"2022-12-10T17:57:31","date_gmt":"2022-12-10T17:57:31","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=23639"},"modified":"2022-12-27T23:59:54","modified_gmt":"2022-12-27T23:59:54","slug":"um-trapezio-retangulo-2","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=23639","title":{"rendered":"Um trap\u00e9zio ret\u00e2ngulo"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_23639' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_23639' class='GTTabs_curr'><a  id=\"23639_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_23639' ><a  id=\"23639_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_23639'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag069-6.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23640\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23640\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag069-6.png\" data-orig-size=\"271,468\" 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=\"8_Pag069-6\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag069-6.png\" class=\"alignright wp-image-23640\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag069-6-174x300.png\" alt=\"\" width=\"180\" height=\"311\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag069-6-174x300.png 174w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag069-6.png 271w\" sizes=\"auto, (max-width: 180px) 100vw, 180px\" \/><\/a>Observa o trap\u00e9zio ret\u00e2ngulo [ABCD].<\/p>\n<ol>\n<li>A \u00e1rea do trap\u00e9zio [ABCD] \u00e9 igual a:<br \/><strong>[A]<\/strong> 46 cm<sup>2<\/sup><br \/><strong>[B]<\/strong> 99 cm<sup>2<\/sup><br \/><strong>[C]<\/strong> 198 cm<sup>2<\/sup><br \/><strong>[D]<\/strong> 220 cm<sup>2<\/sup><\/li>\n<li>Qual \u00e9 o per\u00edmetro do trap\u00e9zio, arredondado \u00e0s unidades?<br \/><strong>[A]<\/strong> 45 cm<br \/><strong>[B]<\/strong> 39 cm<br \/><strong>[C]<\/strong> 53 cm<br \/><strong>[D]<\/strong> 51 cm<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_23639' onClick='GTTabs_show(1,23639)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_23639'>\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\/2022\/12\/8_Pag069-6.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23640\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23640\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag069-6.png\" data-orig-size=\"271,468\" 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=\"8_Pag069-6\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag069-6.png\" class=\"alignright wp-image-23640\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag069-6-174x300.png\" alt=\"\" width=\"180\" height=\"311\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag069-6-174x300.png 174w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag069-6.png 271w\" sizes=\"auto, (max-width: 180px) 100vw, 180px\" \/><\/a>Observa o trap\u00e9zio ret\u00e2ngulo [ABCD].<\/p>\n<\/blockquote>\n<ol>\n<li>\n<blockquote>A \u00e1rea do trap\u00e9zio [ABCD] \u00e9 igual a:<br \/><strong>[A]<\/strong> 46 cm<sup>2<\/sup><br \/><strong>[B]<\/strong> 99 cm<sup>2<\/sup><br \/><strong>[C]<\/strong> 198 cm<sup>2<\/sup><br \/><strong>[D]<\/strong> 220 cm<sup>2<\/sup><\/blockquote>\n<\/li>\n<li>\n<blockquote>Qual \u00e9 o per\u00edmetro do trap\u00e9zio, arredondado \u00e0s unidades?<br \/><strong>[A]<\/strong> 45 cm<br \/><strong>[B]<\/strong> 39 cm<br \/><strong>[C]<\/strong> 53 cm<br \/><strong>[D]<\/strong> 51 cm<\/blockquote>\n<\/li>\n<\/ol>\n<p>\u00a0<\/p>\n<ol>\n<li>A \u00e1rea, em cm<sup>2<\/sup>, do trap\u00e9zio [ABCD] \u00e9:<br \/>\\[{A_{\\left[ {ABCD} \\right]}} = \\frac{{\\overline {BC} + \\overline {AD} }}{2} \\times \\overline {AB} = \\frac{{23 + 10}}{2} \\times 6 = 33 \\times 3 = 99\\]<br \/>Portanto, a op\u00e7\u00e3o correta \u00e9 <strong style=\"color: initial;\">[B]<\/strong><span style=\"color: initial;\"> 99 cm<\/span><sup style=\"color: initial;\">2<\/sup>.<br \/><br \/><\/li>\n<li>Aplicando o Teorema de Pit\u00e1goras, comecemos por determinar o comprimento, em cm, do lado [CD]:<br \/>\\[\\overline {CD} = \\sqrt {{{\\overline {AB} }^2} + {{\\left( {\\overline {BC} &#8211; \\overline {AD} } \\right)}^2}} = \\sqrt {{6^2} + {{\\left( {23 &#8211; 10} \\right)}^2}} = \\sqrt {36 + 169} = \\sqrt {205} \\]<br \/>O per\u00edmetro do trap\u00e9zio, em cent\u00edmetros e arredondado \u00e0s unidades, \u00e9:<br \/>\\[{P_{\\left[ {ABCD} \\right]}} = \\overline {AB} + \\overline {BC} + \\overline {CD} + \\overline {DA} = 6 + 23 + \\sqrt {205} + 10 = 39 + \\sqrt {205} \\approx 53\\]<br \/>Portanto, a op\u00e7\u00e3o correta \u00e9 <strong style=\"color: initial;\">[C]<\/strong><span style=\"color: initial;\"> 53 cm.<\/span><\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_23639' onClick='GTTabs_show(0,23639)'>&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 [ABCD]. A \u00e1rea do trap\u00e9zio [ABCD] \u00e9 igual a:[A] 46 cm2[B] 99 cm2[C] 198 cm2[D] 220 cm2 Qual \u00e9 o per\u00edmetro do trap\u00e9zio, arredondado \u00e0s unidades?[A] 45&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":23641,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,682],"tags":[424,108,67,118],"series":[],"class_list":["post-23639","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-teorema-de-pitagoras","tag-8-o-ano","tag-area","tag-geometria","tag-teorema-de-pitagoras"],"views":309,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag069-6_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23639","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=23639"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23639\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/23641"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=23639"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=23639"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=23639"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=23639"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}