{"id":5102,"date":"2010-11-02T00:08:28","date_gmt":"2010-11-02T00:08:28","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=5102"},"modified":"2022-01-19T17:23:00","modified_gmt":"2022-01-19T17:23:00","slug":"outro-prisma-triangular","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=5102","title":{"rendered":"Outro prisma triangular"},"content":{"rendered":"<p><ul id='GTTabs_ul_5102' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_5102' class='GTTabs_curr'><a  id=\"5102_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_5102' ><a  id=\"5102_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_5102'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag-119-12.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"5103\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=5103\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag-119-12.jpg\" data-orig-size=\"277,441\" 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=\"Prisma triangular\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag-119-12.jpg\" class=\"alignright wp-image-5103\" title=\"Prisma triangular\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag-119-12-188x300.jpg\" alt=\"\" width=\"200\" height=\"318\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag-119-12-188x300.jpg 188w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag-119-12-94x150.jpg 94w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag-119-12.jpg 277w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/><\/a>Na figura est\u00e1 representado um prisma triangular.<\/p>\n<p>Calcula:<\/p>\n<ol>\n<li>a sua \u00e1rea total;<\/li>\n<li>o seu volume;<\/li>\n<li>o volume de uma pir\u00e2mide com a mesma base e a mesma altura.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_5102' onClick='GTTabs_show(1,5102)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_5102'>\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\/pag-119-12.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"5103\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=5103\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag-119-12.jpg\" data-orig-size=\"277,441\" 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=\"Prisma triangular\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag-119-12.jpg\" class=\"alignright wp-image-5103\" title=\"Prisma triangular\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag-119-12-188x300.jpg\" alt=\"\" width=\"200\" height=\"318\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag-119-12-188x300.jpg 188w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag-119-12-94x150.jpg 94w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag-119-12.jpg 277w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/><\/a>A base do prisma \u00e9 um tri\u00e2ngulo ret\u00e2ngulo, cujos lados adjacentes ao \u00e2ngulo reto t\u00eam comprimentos 3 cm e 4cm.<br \/>\nLogo, a \u00e1rea de uma das bases \u00e9 ${{A}_{b}}=\\frac{3\\times 4}{2}=6\\,c{{m}^{2}}$.<\/p>\n<p>A superf\u00edcie lateral \u00e9 constitu\u00edda por 3 ret\u00e2ngulos, todos eles com comprimento 12 cm, mas com larguras 3, 4 e 5 cm.<br \/>\nLogo, a \u00e1rea lateral do prisma \u00e9 ${{A}_{L}}=12\\times 3+12\\times 4+12\\times 5=12\\times (3+4+5)=144\\,c{{m}^{2}}$.<\/p>\n<p>Portanto, a \u00e1rea total do prisma \u00e9 ${{A}_{T}}=2\\times {{A}_{b}}+{{A}_{L}}=2\\times 6+144=156\\,c{{m}^{2}}$.<br \/>\n\u00ad<\/p>\n<\/li>\n<li>\n<p>O volume do prisma \u00e9 $V={{A}_{b}}\\times h=6\\times 12=72\\,c{{m}^{3}}$.<br \/>\n\u00ad<\/p>\n<\/li>\n<li>\n<p>O volume dessa pir\u00e2mide \u00e9 $V&#8217;=\\frac{V}{3}=\\frac{1}{3}\\times {{A}_{b}}\\times h=\\frac{6\\times 12}{3}=24\\,c{{m}^{3}}$.<\/p>\n<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_5102' onClick='GTTabs_show(0,5102)'>&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 sua \u00e1rea total; o seu volume; o volume de uma pir\u00e2mide com a mesma base e a mesma altura. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20652,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,102],"tags":[424,67,109],"series":[],"class_list":["post-5102","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-do-espaco-ao-plano","tag-8-o-ano","tag-geometria","tag-volume"],"views":7119,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/7V2Pag119-12_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/5102","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=5102"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/5102\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20652"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5102"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5102"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5102"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=5102"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}