{"id":13487,"date":"2018-02-05T19:18:24","date_gmt":"2018-02-05T19:18:24","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13487"},"modified":"2022-01-16T14:49:08","modified_gmt":"2022-01-16T14:49:08","slug":"uma-piramide-quadrangular-regular-5","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13487","title":{"rendered":"Uma pir\u00e2mide quadrangular regular"},"content":{"rendered":"<p><ul id='GTTabs_ul_13487' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13487' class='GTTabs_curr'><a  id=\"13487_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13487' ><a  id=\"13487_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_13487'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-3.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13488\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13488\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-3.png\" data-orig-size=\"270,220\" 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=\"Pir\u00e2mide\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-3.png\" class=\"alignright size-full wp-image-13488\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-3.png\" alt=\"\" width=\"270\" height=\"220\" \/><\/a>Considera a seguinte pir\u00e2mide quadrangular regular [ABCDV].<\/p>\n<p>Sabemos que:<\/p>\n<ul>\n<li>a \u00e1rea de cada face lateral \u00e9 60 cm<sup>2<\/sup>;<\/li>\n<li>o comprimento da altura de cada face lateral \u00e9 10 cm;<\/li>\n<li>V&#8217; \u00e9 a proje\u00e7\u00e3o ortogonal de V (v\u00e9rtice da pir\u00e2mide) no plano ABC.<\/li>\n<\/ul>\n<p>Calcula a dist\u00e2ncia de V a V&#8217;.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13487' onClick='GTTabs_show(1,13487)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13487'>\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\/9V2Pag011-3.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13488\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13488\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-3.png\" data-orig-size=\"270,220\" 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=\"Pir\u00e2mide\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-3.png\" class=\"alignright size-full wp-image-13488\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-3.png\" alt=\"\" width=\"270\" height=\"220\" \/><\/a>Seja M o ponto m\u00e9dio da aresta [BC].<\/p>\n<p>Comecemos por determinar o comprimento (em cm) da aresta da base da pir\u00e2mide:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{{A_{fL}} = 60}&amp; \\Leftrightarrow &amp;{\\frac{{\\overline {BC} \\times \\overline {VM} }}{2} = 60}\\\\{}&amp; \\Leftrightarrow &amp;{\\frac{{\\overline {BC} \\times 10}}{2} = 60}\\\\{}&amp; \\Leftrightarrow &amp;{\\overline {BC} = 12}\\end{array}\\]<\/p>\n<p>Aplicando o Teorema de Pit\u00e1goras no tri\u00e2ngulo ret\u00e2ngulo [VMV&#8217;], vem:<\/p>\n<p>\\[\\overline {VV&#8217;} = \\sqrt {{{\\overline {VM} }^2} &#8211; {{\\overline {MV&#8217;} }^2}} = \\sqrt {{{10}^2} &#8211; {6^2}} = \\sqrt {64} = 8\\]<\/p>\n<p>Portanto,\u00a0a dist\u00e2ncia de V a V&#8217; \u00e9 8 cm.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13487' onClick='GTTabs_show(0,13487)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considera a seguinte pir\u00e2mide quadrangular regular [ABCDV]. Sabemos que: a \u00e1rea de cada face lateral \u00e9 60 cm2; o comprimento da altura de cada face lateral \u00e9 10 cm; V&#8217; \u00e9&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20367,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,466],"tags":[426,467],"series":[],"class_list":["post-13487","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-distancia"],"views":2635,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-3_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13487","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=13487"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13487\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20367"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13487"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13487"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13487"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13487"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}