{"id":13787,"date":"2018-03-04T23:42:01","date_gmt":"2018-03-04T23:42:01","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13787"},"modified":"2022-01-16T18:33:18","modified_gmt":"2022-01-16T18:33:18","slug":"um-prisma-triangular","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13787","title":{"rendered":"Um prisma triangular"},"content":{"rendered":"<p><ul id='GTTabs_ul_13787' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13787' class='GTTabs_curr'><a  id=\"13787_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13787' ><a  id=\"13787_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_13787'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag25-6.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13788\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13788\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag25-6.png\" data-orig-size=\"285,485\" 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\/9V2Pag25-6.png\" class=\"alignright size-medium wp-image-13788\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag25-6-176x300.png\" alt=\"\" width=\"176\" height=\"300\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag25-6-176x300.png 176w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag25-6.png 285w\" sizes=\"auto, (max-width: 176px) 100vw, 176px\" \/><\/a>Na figura est\u00e1 representado um prisma triangular.<\/p>\n<p>Calcula:<\/p>\n<ol>\n<li>a \u00e1rea da sua superf\u00edcie;<\/li>\n<li>o seu volume;<\/li>\n<li>o volume de uma pir\u00e2mide com a mesma base e a mesma altura do prisma.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13787' onClick='GTTabs_show(1,13787)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13787'>\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\/03\/9V2Pag25-6.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13788\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13788\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag25-6.png\" data-orig-size=\"285,485\" 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\/9V2Pag25-6.png\" class=\"alignright size-medium wp-image-13788\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag25-6-176x300.png\" alt=\"\" width=\"176\" height=\"300\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag25-6-176x300.png 176w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag25-6.png 285w\" sizes=\"auto, (max-width: 176px) 100vw, 176px\" \/><\/a>A\u00a0\u00e1rea da superf\u00edcie do prima \u00e9 156 cm<sup>2<\/sup>:<br \/>\n\\[\\begin{array}{*{20}{l}}{{A_T}}&amp; = &amp;{2 \\times {A_{Base}} + {A_{Lateral}}}\\\\{}&amp; = &amp;{2 \\times \\frac{{\\overline {BC} \\times \\overline {AC} }}{2} + \\left( {\\overline {AB} + \\overline {BC} + \\overline {CA} } \\right) \\times \\overline {AE} }\\\\{}&amp; = &amp;{2 \\times \\frac{{3 \\times 4}}{2} + \\left( {5 + 3 + 4} \\right) \\times 12}\\\\{}&amp; = &amp;{156}\\end{array}\\]<\/li>\n<li>O volume do prisma \u00e9 72 cm<sup>3<\/sup>:<br \/>\n\\[\\begin{array}{*{20}{l}}{{V_{Prisma}}}&amp; = &amp;{\\frac{{\\overline {BC} \\times \\overline {AC} }}{2} \\times \\overline {AE} }\\\\{}&amp; = &amp;{\\frac{{3 \\times 4}}{2} \\times 12}\\\\{}&amp; = &amp;{72}\\end{array}\\]<\/li>\n<li>O\u00a0volume de uma pir\u00e2mide com a mesma base e a mesma altura do prisma \u00e9 24 cm<sup>3<\/sup>:<br \/>\n\\[\\begin{array}{*{20}{l}}{{V_{Pir\u00e2mide}}}&amp; = &amp;{\\frac{1}{3} \\times {V_{Prisma}}}\\\\{}&amp; = &amp;{\\frac{1}{3} \\times \\frac{{\\overline {BC} \\times \\overline {AC} }}{2} \\times \\overline {AE} }\\\\{}&amp; = &amp;{\\frac{1}{3} \\times \\frac{{3 \\times 4}}{2} \\times 12}\\\\{}&amp; = &amp;{24}\\end{array}\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13787' onClick='GTTabs_show(0,13787)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Na figura est\u00e1 representado um prisma triangular. Calcula: a \u00e1rea da sua superf\u00edcie; o seu volume; o volume de uma pir\u00e2mide com a mesma base e a mesma altura do prisma.&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20398,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,466],"tags":[426,108,468,109],"series":[],"class_list":["post-13787","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","tag-volume"],"views":2846,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag025-6-b_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13787","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=13787"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13787\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20398"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13787"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13787"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13787"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13787"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}