{"id":6423,"date":"2010-12-25T17:09:47","date_gmt":"2010-12-25T17:09:47","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6423"},"modified":"2022-01-19T19:29:48","modified_gmt":"2022-01-19T19:29:48","slug":"um-prisma","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6423","title":{"rendered":"Um prisma"},"content":{"rendered":"<p><ul id='GTTabs_ul_6423' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6423' class='GTTabs_curr'><a  id=\"6423_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6423' ><a  id=\"6423_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_6423'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/pag-39-4.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6424\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6424\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/pag-39-4.jpg\" data-orig-size=\"251,395\" 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\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/pag-39-4.jpg\" class=\"alignright wp-image-6424\" title=\"Prisma\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/pag-39-4.jpg\" alt=\"\" width=\"200\" height=\"315\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/pag-39-4.jpg 251w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/pag-39-4-190x300.jpg 190w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/pag-39-4-95x150.jpg 95w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/><\/a>Observa o prisma representado na figura:<\/p>\n<ol>\n<li>Indica, usando as letras da figura:<br \/>\n&#8211; duas retas paralelas;<br \/>\n&#8211; dois planos perpendiculares;<br \/>\n&#8211; \u00a0uma reta e um plano perpendiculares;<br \/>\n&#8211; dois planos paralelos;<br \/>\n&#8211; uma reta paralela a um plano.<\/li>\n<li>Calcula o volume do prisma.<\/li>\n<li>Determina um valor aproximado \u00e0s unidades da \u00e1rea total do prisma.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6423' onClick='GTTabs_show(1,6423)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6423'>\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\/12\/pag-39-4.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6424\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6424\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/pag-39-4.jpg\" data-orig-size=\"251,395\" 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\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/pag-39-4.jpg\" class=\"alignright wp-image-6424\" title=\"Prisma\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/pag-39-4.jpg\" alt=\"\" width=\"200\" height=\"315\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/pag-39-4.jpg 251w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/pag-39-4-190x300.jpg 190w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/pag-39-4-95x150.jpg 95w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/><\/a>Por exemplo:<br \/>\n&#8211; as retas ED e FG s\u00e3o paralelas;<br \/>\n&#8211; os planos ABG e DEF s\u00e3o perpendiculares;<br \/>\n&#8211; a reta EF \u00e9 perpendicular ao plano ABG;<br \/>\n&#8211; os planos ABF e CDE s\u00e3o paralelos;<br \/>\n&#8211; a reta AB \u00e9 paralela ao plano CDE.<br \/>\n\u00ad<\/li>\n<li>A \u00e1rea da base do prisma (trap\u00e9zio [ABGF]) \u00e9: ${{A}_{b}}=\\frac{2,5+1,5}{2}\\times 3=2\\times 3=6\\,c{{m}^{2}}$.\n<p>Logo, o volume do prisma \u00e9: $V=6\\times 4=24\\,c{{m}^{3}}$.<br \/>\n\u00ad<\/p>\n<\/li>\n<li>Admitindo que a base do prisma \u00e9 um trap\u00e9zio is\u00f3sceles, temos: $\\overline{AF}=\\overline{BG}=\\sqrt{{{3}^{2}}+{{(0,5)}^{2}}}=\\sqrt{9,25}$.\n<p>A \u00e1rea lateral \u00e9: ${{A}_{L}}=1\\times (1,5\\times 4)+1\\times (2,5\\times 4)+2\\times (\\sqrt{9,25}\\times 4)=(16+8\\times \\sqrt{9,25})\\,c{{m}^{2}}$.<\/p>\n<p>A \u00e1rea total do prisma \u00e9: $A=2\\times 6+16+8\\times \\sqrt{9,25}=28+8\\times \\sqrt{9,25}\\simeq 52\\,c{{m}^{2}}$.<\/p>\n<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6423' onClick='GTTabs_show(0,6423)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Observa o prisma representado na figura: Indica, usando as letras da figura: &#8211; duas retas paralelas; &#8211; dois planos perpendiculares; &#8211; \u00a0uma reta e um plano perpendiculares; &#8211; dois planos paralelos;&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20682,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,112],"tags":[424,67,118],"series":[],"class_list":["post-6423","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-geometria","tag-teorema-de-pitagoras"],"views":3019,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/8V1Pag039-4_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6423","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=6423"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6423\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20682"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6423"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6423"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6423"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6423"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}