{"id":13496,"date":"2018-02-05T21:23:55","date_gmt":"2018-02-05T21:23:55","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13496"},"modified":"2022-01-16T15:04:45","modified_gmt":"2022-01-16T15:04:45","slug":"um-prisma-hexagonal","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13496","title":{"rendered":"Um prisma hexagonal"},"content":{"rendered":"<p><ul id='GTTabs_ul_13496' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13496' class='GTTabs_curr'><a  id=\"13496_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13496' ><a  id=\"13496_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_13496'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Um prisma reto tem por base um hex\u00e1gono regular, cujo lado mede 10 cm.<\/p>\n<p>Determina o volume desse prisma, sabendo que tem 80 cm de altura.<br \/>\nApresenta o resultado arredondado \u00e0s cent\u00e9simas.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13496' onClick='GTTabs_show(1,13496)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13496'>\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\/02\/Hexagonal_prism.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13498\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13498\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/Hexagonal_prism.png\" data-orig-size=\"554,480\" 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 hexagonal\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/Hexagonal_prism.png\" class=\"alignright wp-image-13498\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/Hexagonal_prism-300x260.png\" alt=\"\" width=\"260\" height=\"225\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/Hexagonal_prism-300x260.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/Hexagonal_prism.png 554w\" sizes=\"auto, (max-width: 260px) 100vw, 260px\" \/><\/a>Como se sabe, o hex\u00e1gono regular \u00e9 decompon\u00edvel em seis tri\u00e2ngulos equil\u00e1teros geometricamente iguais, de lado igual ao lado do hex\u00e1gono.<br \/>\n(Para rever, consultar <a href=\"https:\/\/www.acasinhadamatematica.pt\/?p=13453\" target=\"_blank\" rel=\"noopener\">aqui<\/a>)<\/p>\n<p>Comecemos por determinar a altura desse tri\u00e2ngulo equil\u00e1tero (ap\u00f3tema do hex\u00e1gono), por aplica\u00e7\u00e3o do Teorema de Pit\u00e1goras:<\/p>\n<p>\\[ap = \\sqrt {{{10}^2} &#8211; {5^2}} = \\sqrt {75} = 5\\sqrt 3 \\]<\/p>\n<p>Assim, o volume do prisma considerado, em cent\u00edmetros c\u00fabicos, \u00e9:<\/p>\n<p>\\[{V_{Prisma}} = 6 \\times \\frac{{10 \\times 5\\sqrt 3 }}{2} \\times 80 = 12000\\sqrt 3 \\approx 20784,61\\]<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13496' onClick='GTTabs_show(0,13496)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Um prisma reto tem por base um hex\u00e1gono regular, cujo lado mede 10 cm. Determina o volume desse prisma, sabendo que tem 80 cm de altura. Apresenta o resultado arredondado \u00e0s&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20369,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,466],"tags":[426,468,109],"series":[],"class_list":["post-13496","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-prisma","tag-volume"],"views":2895,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag016-4_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13496","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=13496"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13496\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20369"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13496"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13496"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13496"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13496"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}