{"id":13761,"date":"2018-03-03T23:25:07","date_gmt":"2018-03-03T23:25:07","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13761"},"modified":"2022-01-16T18:18:56","modified_gmt":"2022-01-16T18:18:56","slug":"um-prisma-quadrangular-regular-3","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13761","title":{"rendered":"Um prisma quadrangular regular"},"content":{"rendered":"<p><ul id='GTTabs_ul_13761' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13761' class='GTTabs_curr'><a  id=\"13761_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13761' ><a  id=\"13761_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_13761'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Prisma3x3x4.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13762\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13762\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Prisma3x3x4.png\" data-orig-size=\"343,432\" 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=\"Prisma\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Prisma3x3x4.png\" class=\"alignright size-medium wp-image-13762\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Prisma3x3x4-238x300.png\" alt=\"\" width=\"238\" height=\"300\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Prisma3x3x4-238x300.png 238w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Prisma3x3x4.png 343w\" sizes=\"auto, (max-width: 238px) 100vw, 238px\" \/><\/a>Considera um prisma quadrangular regular cuja base tem 12 cm de per\u00edmetro e a medida da aresta lateral \u00e9 a ter\u00e7a parte do per\u00edmetro da base.<\/p>\n<ol>\n<li>Calcula a \u00e1rea da sua superf\u00edcie lateral.<\/li>\n<li>Determina o volume do prisma.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13761' onClick='GTTabs_show(1,13761)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13761'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/2017-18-MF9P2-pag25-2.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13764\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13764\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/2017-18-MF9P2-pag25-2.png\" data-orig-size=\"525,397\" 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=\"Planifica\u00e7\u00e3o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/2017-18-MF9P2-pag25-2.png\" class=\"aligncenter wp-image-13764 size-full\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/2017-18-MF9P2-pag25-2.png\" alt=\"\" width=\"525\" height=\"397\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/2017-18-MF9P2-pag25-2.png 525w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/2017-18-MF9P2-pag25-2-300x227.png 300w\" sizes=\"auto, (max-width: 525px) 100vw, 525px\" \/><\/a><\/p>\n<ol>\n<li>Como o per\u00edmetro da base \u00e9 12 cm, ent\u00e3o \\(\\overline {AB} = \\overline {BC} = \\overline {CD} = \\overline {DA} = \\frac{{12}}{4} = 3\\)\u00a0 cm.\n<p>Como\u00a0a medida da aresta lateral \u00e9 a ter\u00e7a parte do per\u00edmetro da base, ent\u00e3o\u00a0\\(\\overline {AE} = \\overline {BF} = \\overline {CG} = \\overline {DH} = \\frac{{12}}{3} = 4\\)\u00a0 cm.<\/p>\n<p>Assim, a \u00e1rea da superf\u00edcie lateral\u00a0\u00e9 \\({A_L} = 4 \\times \\left( {\\overline {AB} \\times \\overline {AE} } \\right) = 4 \\times \\left( {3 \\times 4} \\right) = 48\\)\u00a0 cm<sup>2<\/sup>.<\/p>\n<\/li>\n<li>O prisma tem \\(V = \\left( {\\overline {AB} \\times \\overline {BC} } \\right) \\times \\overline {AE} = \\left( {3 \\times 3} \\right) \\times 4 = 36\\)\u00a0 cm<sup>3<\/sup> de volume.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13761' onClick='GTTabs_show(0,13761)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considera um prisma quadrangular regular cuja base tem 12 cm de per\u00edmetro e a medida da aresta lateral \u00e9 a ter\u00e7a parte do per\u00edmetro da base. Calcula a \u00e1rea da sua&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20394,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,466],"tags":[426,108,468],"series":[],"class_list":["post-13761","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-distancias-areas-e-volumes-de-solidos","tag-9-o-ano","tag-area","tag-prisma"],"views":4749,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag025-2_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13761","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=13761"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13761\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20394"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13761"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13761"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13761"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13761"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}