{"id":13913,"date":"2018-03-08T01:07:55","date_gmt":"2018-03-08T01:07:55","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13913"},"modified":"2022-01-15T01:50:49","modified_gmt":"2022-01-15T01:50:49","slug":"no-prisma-a-base-e-um-losango-2","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13913","title":{"rendered":"No prisma, a base \u00e9 um losango"},"content":{"rendered":"<p><ul id='GTTabs_ul_13913' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13913' class='GTTabs_curr'><a  id=\"13913_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13913' ><a  id=\"13913_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_13913'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag033-17b.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13915\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13915\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag033-17b.png\" data-orig-size=\"330,245\" 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\/9V2Pag033-17b.png\" class=\"alignright size-medium wp-image-13915\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag033-17b-300x223.png\" alt=\"\" width=\"300\" height=\"223\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag033-17b-300x223.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag033-17b.png 330w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>No prisma seguinte, a base \u00e9 um losango cuja diagonal maior mede 24 cm e cuja diagonal menor mede 10 cm.<\/p>\n<p>Determina:<\/p>\n<ol>\n<li>a \u00e1rea da base;<\/li>\n<li>o volume do prisma;<\/li>\n<li>a \u00e1rea da superf\u00edcie do prisma.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13913' onClick='GTTabs_show(1,13913)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13913'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>A base \u00e9 um losango cujos comprimentos das diagonais s\u00e3o 24 cm e 10 cm.\n<p>Logo, a \u00e1rea da base do prisma \u00e9 ${{A}_{b}}=\\frac{D\\times d}{2}=\\frac{24\\times 10}{2}=120\\,c{{m}^{2}}$.<\/p>\n<\/li>\n<li>O volume do prisma \u00e9 \\(V = \\frac{{24 \\times 10}}{2} \\times 20 = 2400\\;c{m^3}\\).<br \/>\n\u00ad<\/li>\n<li>A superf\u00edcie lateral do prisma \u00e9 constitu\u00edda por quatro ret\u00e2ngulos geometricamente iguais, com as dimens\u00f5es $13\\,cm\\times 20\\,cm$. Logo, a \u00e1rea lateral do prisma \u00e9 ${{A}_{L}}=4\\times (13\\times 20)=1040\\,c{{m}^{2}}$.<br \/>\nPortanto a \u00e1rea total do prisma \u00e9 \\({A_T} = 2 \\times 120 + 1040 = 1280\\;{\\mkern 1mu} c{m^2}\\).<br \/>\n\u00ad<\/li>\n<\/ol>\n<p style=\"text-align: center;\"><script src=\"https:\/\/cdn.geogebra.org\/apps\/deployggb.js\"><\/script>\r\n<div id=\"ggbApplet\" style=\"margin: 0 auto;\"><\/div>\r\n<script>\r\nvar parameters = {\r\n\"id\": \"ggbApplet\",\r\n\"width\":910,\r\n\"height\":520,\r\n\"showMenuBar\":false,\r\n\"showAlgebraInput\":false,\r\n\"showToolBar\":false,\r\n\"customToolBar\":\"0 39 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24  20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49  50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 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is3D=is 3D applet using 3D view, AV=Algebra View, SV=Spreadsheet View, CV=CAS View, EV2=Graphics View 2, CP=Construction Protocol, PC=Probability Calculator, DA=Data Analysis, FI=Function Inspector, PV=Python, macro=Macro View\r\nvar views = {'is3D': 0,'AV': 0,'SV': 0,'CV': 0,'EV2': 0,'CP': 1,'PC': 0,'DA': 0,'FI': 0,'PV': 0,'macro': 0};\r\nvar applet = new GGBApplet(parameters, '5.0', views);\r\nwindow.onload = function() {applet.inject('ggbApplet')};\r\n<\/script><\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13913' onClick='GTTabs_show(0,13913)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado No prisma seguinte, a base \u00e9 um losango cuja diagonal maior mede 24 cm e cuja diagonal menor mede 10 cm. 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