{"id":10602,"date":"2021-03-13T10:04:00","date_gmt":"2021-03-13T10:04:00","guid":{"rendered":"http:\/\/www.max-sperling.bplaced.net\/?p=10602"},"modified":"2021-03-13T10:04:00","modified_gmt":"2021-03-13T10:04:00","slug":"geometry-example-1","status":"publish","type":"post","link":"http:\/\/www.max-sperling.bplaced.net\/?p=10602","title":{"rendered":"Math &#8211; Exercise 1 (Geometry)"},"content":{"rendered":"<p><strong>Given<\/strong><br \/>\n<img decoding=\"async\" src=\"http:\/\/www.max-sperling.bplaced.net\/wp-content\/uploads\/2021\/03\/Geometry_1.svg\" class=\"aligncenter\" \/><\/p>\n<p class=\"aligncenter\">\n\tThe unit of length is cm.<br \/>\n  Figure not drawn to scale.\n<\/p>\n<hr>\n<p><strong>Find<\/strong><br \/>\n<center>The size of the green surface.<\/center><\/p>\n<hr>\n<p><strong>Solution<\/strong><br \/>\n<center><br \/>\n\\(<br \/>\n\\begin{array}{l}<br \/>\n  A_{Green}=A_{\\triangle{ABC}}-(A_{\\triangle{A}}+A_{\\triangle{B}}+A_{\\triangle{C}}) \\\\\\\\<br \/>\n  \\text{Assume}\\ \\angle{CAB} = 90\u00b0 \\\\<br \/>\n  \\overline{CA}^2 + \\overline{AB}^2 = \\overline{BC}^2 \\\\<br \/>\n  (15\\ cm)^2 + (20\\ cm)^2 = (25\\ cm)^2 \\\\<br \/>\n  625\\ cm^2 = 625\\ cm^2\\ \\text{true.} \\\\\\\\<br \/>\n  A_{\\triangle\\ ABC} = \\frac{[AB] \\cdot [AC]}{2} = 150\\ cm^2 \\\\<br \/>\n  A_{\\triangle{A}} = \\frac{(5\\ cm)^2}{2} = 12,5\\ cm^2 \\\\<br \/>\n  A_{\\triangle{B}} = \\frac{(5\\ cm)^2}{2} \\cdot sin(\\angle{ABC}) = 12,5\\ cm^2 \\cdot \\frac{[AC]}{[BC]} = 7,5\\ cm^2 \\\\<br \/>\n  A_{\\triangle{C}} = \\frac{(5\\ cm)^2}{2} \\cdot sin(\\angle{ACB}) = 12,5\\ cm^2 \\cdot \\frac{[AB]}{[BC]} = 10\\ cm^2 \\\\<br \/>\n  A_{Green} = 150\\ cm^2 &#8211; (12,5\\ cm^2 + 7,5\\ cm^2 + 10\\ cm^2) = 120\\ cm^2<br \/>\n\\end{array}<br \/>\n\\)<br \/>\n<\/center><\/p>\n<hr>\n<p><strong>Answer<\/strong><br \/>\n<center>\\(A_{Green} = 120\\ cm^2\\)<\/center><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Given The unit of length is cm. Figure not drawn to scale. Find The size of the green surface. Solution<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false},"categories":[47],"tags":[],"_links":{"self":[{"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=\/wp\/v2\/posts\/10602"}],"collection":[{"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=10602"}],"version-history":[{"count":0,"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=\/wp\/v2\/posts\/10602\/revisions"}],"wp:attachment":[{"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=10602"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=10602"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=10602"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}