{"id":9808,"date":"2012-10-02T17:02:38","date_gmt":"2012-10-02T16:02:38","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=9808"},"modified":"2022-01-20T18:44:17","modified_gmt":"2022-01-20T18:44:17","slug":"determine-a-area-sombreada","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=9808","title":{"rendered":"Determine a \u00e1rea sombreada"},"content":{"rendered":"<p><ul id='GTTabs_ul_9808' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_9808' class='GTTabs_curr'><a  id=\"9808_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_9808' ><a  id=\"9808_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_9808'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>\u00a0Determine a \u00e1rea sombreada a azul em cada figura:<\/p>\n<p>\u00a0<a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/3areas.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"9811\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=9811\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/3areas.jpg\" data-orig-size=\"588,161\" 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=\"\u00c1reas\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/3areas.jpg\" class=\"aligncenter size-full wp-image-9811\" title=\"\u00c1reas\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/3areas.jpg\" alt=\"\" width=\"588\" height=\"161\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/3areas.jpg 588w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/3areas-300x82.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/3areas-150x41.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/3areas-400x109.jpg 400w\" sizes=\"auto, (max-width: 588px) 100vw, 588px\" \/><\/a><\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_9808' onClick='GTTabs_show(1,9808)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_9808'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/3areas.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"9811\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=9811\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/3areas.jpg\" data-orig-size=\"588,161\" 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=\"\u00c1reas\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/3areas.jpg\" class=\"aligncenter size-full wp-image-9811\" title=\"\u00c1reas\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/3areas.jpg\" alt=\"\" width=\"588\" height=\"161\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/3areas.jpg 588w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/3areas-300x82.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/3areas-150x41.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/3areas-400x109.jpg 400w\" sizes=\"auto, (max-width: 588px) 100vw, 588px\" \/><\/a><\/p>\n<\/p>\n<p>Na respetiva unidade de \u00e1rea, vem sucessivamente:<\/p>\n<p>$$\\begin{array}{*{20}{l}} {{A_{Azul}}}&amp; = &amp;{{A_{C\u00edrculo}} &#8211; {A_{{\\mathop{\\rm Re}\\nolimits} t\u00e2ngulo}}}\\\\ {}&amp; = &amp;{\\pi\u00a0 \\times {5^2} &#8211; \\left( {2 \\times 4} \\right) \\times \\left( {2 \\times 3} \\right)}\\\\ {}&amp; = &amp;{25\\pi\u00a0 &#8211; 48} \\end{array}$$<\/p>\n<\/p>\n<p>$$\\begin{array}{*{20}{l}} {{A_{Azul}}}&amp; = &amp;{{A_{C\u00edrculo}} &#8211; {A_{Tri\u00e2ngulo}}}\\\\ {}&amp; = &amp;{\\pi\u00a0 \\times {{10}^2} &#8211; \\frac{{\\left( {2 \\times 6} \\right) \\times \\left( {10 + 8} \\right)}}{2}}\\\\ {}&amp; = &amp;{100\\pi\u00a0 &#8211; 108} \\end{array}$$<\/p>\n<\/p>\n<p>$$\\begin{array}{*{20}{l}} {{A_{Azul}}}&amp; = &amp;{\\frac{{{A_{C\u00edrculo Grande}}}}{2} &#8211; {A_{C\u00edrculo Pequeno}}}\\\\ {}&amp; = &amp;{\\frac{{\\pi\u00a0 \\times {{14}^2}}}{2} &#8211; \\pi\u00a0 \\times {7^2}}\\\\ {}&amp; = &amp;{98\\pi\u00a0 &#8211; 49\\pi }\\\\ {}&amp; = &amp;{49\\pi } \\end{array}$$<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_9808' onClick='GTTabs_show(0,9808)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado \u00a0Determine a \u00e1rea sombreada a azul em cada figura: \u00a0 Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20761,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[321,97,322],"tags":[429,324,430],"series":[],"class_list":["post-9808","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-10-o-ano","category-aplicando","category-modulo-inicial","tag-10-o-ano","tag-areas","tag-modulo-inicial"],"views":2859,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/10V1Pag033-3_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/9808","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=9808"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/9808\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20761"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9808"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9808"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9808"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=9808"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}