{"id":11331,"date":"2012-11-12T19:56:17","date_gmt":"2012-11-12T19:56:17","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=11331"},"modified":"2022-01-20T02:09:58","modified_gmt":"2022-01-20T02:09:58","slug":"um-sinal-de-transito","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=11331","title":{"rendered":"Um sinal de tr\u00e2nsito"},"content":{"rendered":"<p><ul id='GTTabs_ul_11331' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_11331' class='GTTabs_curr'><a  id=\"11331_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_11331' ><a  id=\"11331_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_11331'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/sinaltransito.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"11334\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=11334\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/sinaltransito.jpg\" data-orig-size=\"147,147\" 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;}\" data-image-title=\"Sinal de tr\u00e2nsito\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/sinaltransito.jpg\" class=\"alignright size-full wp-image-11334\" title=\"Sinal de tr\u00e2nsito\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/sinaltransito.jpg\" alt=\"\" width=\"147\" height=\"147\" \/><\/a>A Maria pintou um sinal de tr\u00e2nsito com a forma de um quadrado de $2116$ cm<sup>2<\/sup> de \u00e1rea.<\/p>\n<p>Qual a \u00e1rea da parte azul da figura?<br \/>\nApresenta todos os c\u00e1lculos efetuados e explica a tua resposta.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_11331' onClick='GTTabs_show(1,11331)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_11331'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/7ano-pag38-sinaltransito.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"11336\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=11336\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/7ano-pag38-sinaltransito.png\" data-orig-size=\"610,259\" 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;}\" data-image-title=\"Sinal de tr\u00e2nsito\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/7ano-pag38-sinaltransito.png\" class=\"aligncenter  wp-image-11336\" title=\"Sinal de tr\u00e2nsito\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/7ano-pag38-sinaltransito.png\" alt=\"\" width=\"366\" height=\"155\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/7ano-pag38-sinaltransito.png 610w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/7ano-pag38-sinaltransito-300x127.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/7ano-pag38-sinaltransito-150x63.png 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/7ano-pag38-sinaltransito-400x169.png 400w\" sizes=\"auto, (max-width: 366px) 100vw, 366px\" \/><\/a><\/p>\n<\/p>\n<p>A simetria da figura relativamente \u00e0s zonas pintadas a azul e a branco, permite perceber que o quadrado est\u00e1 dividido em $4$ tri\u00e2ngulos ret\u00e2ngulos geometricamente iguais. Como dois deles foram pintados de cor azul, ent\u00e3o a \u00e1rea da parte azul da figura \u00e9 metade da \u00e1rea do quadrado.<\/p>\n<p>Assim, a parte azul da figura tem ${A_{Azul}} = \\frac{{{A_\\square }}}{2} = \\frac{{2116}}{2} = 1058$ cm<sup>2<\/sup> de \u00e1rea.<\/p>\n<\/p>\n<h4>\u00ad<\/h4>\n<h4 style=\"text-align: center;\">Nota Importante<\/h4>\n<p>Pode ficar a ideia de que o valor da \u00e1rea da parte azul da figura se deve ao facto de o quadrado original ter ficado divido em $4$ tri\u00e2ngulos ret\u00e2ngulos geometricamente iguais.<\/p>\n<p>Ora, essa ideia n\u00e3o corresponde \u00e0 verdade, como podes constatar na anima\u00e7\u00e3o seguinte, deslocando o ponto $P$. Tenta justificar o que observas.<\/p>\n<\/p>\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\":344,\r\n\"height\":344,\r\n\"showMenuBar\":false,\r\n\"showAlgebraInput\":false,\r\n\"showToolBar\":false,\r\n\"customToolBar\":\"0 39 59 || 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 , 14 66 68 | 25 52 60 61 || 40 41 42 , 27 28 35 , 6\",\r\n\"showToolBarHelp\":false,\r\n\"showResetIcon\":true,\r\n\"enableLabelDrags\":false,\r\n\"enableShiftDragZoom\":false,\r\n\"enableRightClick\":false,\r\n\"errorDialogsActive\":false,\r\n\"useBrowserForJS\":false,\r\n\"preventFocus\":false,\r\n\"showFullscreenButton\":true,\r\n\"language\":\"pt\",\r\n\/\/ use this 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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>\n<p style=\"text-align: left;\">\n<p style=\"text-align: left;\">\u00c9 \u00fatil teres presente:<\/p>\n<p style=\"text-align: left;\">$${A_{Quadrado}} = Base \\times Altura$$<\/p>\n<p style=\"text-align: left;\">$${A_{Tri\u00e2ngulo}} = \\frac{{Base \\times Altura}}{2}$$<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_11331' onClick='GTTabs_show(0,11331)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado A Maria pintou um sinal de tr\u00e2nsito com a forma de um quadrado de $2116$ cm2 de \u00e1rea. Qual a \u00e1rea da parte azul da figura? 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