{"id":23506,"date":"2022-12-08T20:03:38","date_gmt":"2022-12-08T20:03:38","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=23506"},"modified":"2022-12-27T23:55:31","modified_gmt":"2022-12-27T23:55:31","slug":"um-papagaio-de-papel","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=23506","title":{"rendered":"Um papagaio de papel"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_23506' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_23506' class='GTTabs_curr'><a  id=\"23506_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_23506' ><a  id=\"23506_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_23506'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-10.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23507\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23507\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-10.png\" data-orig-size=\"209,275\" 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=\"8_Pag066-10\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-10.png\" class=\"alignright wp-image-23507\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-10.png\" alt=\"\" width=\"180\" height=\"237\" \/><\/a>Observa o papagaio de papel [ABCD].<\/p>\n<p>\\(\\overline {AB} = 5,4\\) cm; \\(\\overline {BC} = 8,5\\) cm e \\(\\overline {BD} = 7,6\\).<\/p>\n<ol>\n<li>Calcula o per\u00edmetro do papagaio.<\/li>\n<li>Qual \u00e9 a \u00e1rea de papel gasto no papagaio?<br \/>(Sempre que necess\u00e1rio, usa valores aproximados \u00e0s d\u00e9cimas.)<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_23506' onClick='GTTabs_show(1,23506)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_23506'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-10_Diagonais.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23510\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23510\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-10_Diagonais.png\" data-orig-size=\"548,745\" 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=\"8_Pag066-10_Diagonais\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-10_Diagonais.png\" class=\"alignright wp-image-23510\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-10_Diagonais-221x300.png\" alt=\"\" width=\"240\" height=\"326\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-10_Diagonais-221x300.png 221w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-10_Diagonais.png 548w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a>Observa o papagaio de papel [ABCD].<\/p>\n<p>\\(\\overline {AB} = 5,4\\) cm; \\(\\overline {BC} = 8,5\\) cm e \\(\\overline {BD} = 7,6\\).<\/p>\n<\/blockquote>\n<ol>\n<li>\n<blockquote>Calcula o per\u00edmetro do papagaio.<\/blockquote>\n<\/li>\n<li>\n<blockquote>Qual \u00e9 a \u00e1rea de papel gasto no papagaio?<br \/>(Sempre que necess\u00e1rio, usa valores aproximados \u00e0s d\u00e9cimas.)<\/blockquote>\n<\/li>\n<\/ol>\n<p>\u00a0<\/p>\n<ol>\n<li>O papagaio tem \\(P = 2 \\times \\left( {\\overline {AB} + \\overline {BC} } \\right) = 2 \\times \\left( {5,4 + 8,5} \\right) = 27,8\\) cm de per\u00edmetro.<br \/><br \/><\/li>\n<li>Comecemos por determinar o comprimento (em cm) da diagonal maior do papagaio, por aplica\u00e7\u00e3o do Teorema de Pit\u00e1goras nos tri\u00e2ngulos [ABF] e [BCF]:<br \/>\\[\\begin{array}{*{20}{l}}{\\overline {AC} }&amp; = &amp;{\\overline {AF} + \\overline {CF} }\\\\{}&amp; = &amp;{\\sqrt {{{\\overline {AB} }^2} &#8211; {{\\overline {BF} }^2}} + \\sqrt {{{\\overline {BC} }^2} &#8211; {{\\overline {BF} }^2}} }\\\\{}&amp; = &amp;{\\sqrt {{{5,4}^2} &#8211; {{3,8}^2}} + \\sqrt {{{8,5}^2} &#8211; {{3,8}^2}} }\\\\{}&amp; = &amp;{\\sqrt {14,72} + \\sqrt {57,81} }\\end{array}\\]<br \/>Determinemos, agora, a \u00e1rea (em cm<sup>2<\/sup>) do papagaio:<br \/>\\[A = \\frac{{\\overline {AC} \\times \\overline {BD} }}{2} = \\frac{{\\left( {\\sqrt {14,72} + \\sqrt {57,81} } \\right) \\times 7,6}}{2} = \\left( {\\sqrt {14,72} + \\sqrt {57,81} } \\right) \\times 3,8 \\approx 43,47\\]<br \/>Portanto, foi gasto no papagaio cerca de 43, 47 cm<sup>2<\/sup> de papel.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_23506' onClick='GTTabs_show(0,23506)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Observa o papagaio de papel [ABCD]. \\(\\overline {AB} = 5,4\\) cm; \\(\\overline {BC} = 8,5\\) cm e \\(\\overline {BD} = 7,6\\). Calcula o per\u00edmetro do papagaio. Qual \u00e9 a \u00e1rea de&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":23508,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,682],"tags":[424,67,118],"series":[],"class_list":["post-23506","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-teorema-de-pitagoras","tag-8-o-ano","tag-geometria","tag-teorema-de-pitagoras"],"views":263,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-10_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23506","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=23506"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23506\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/23508"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=23506"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=23506"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=23506"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=23506"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}