{"id":280987,"date":"2025-08-05T10:05:21","date_gmt":"2025-08-05T10:05:21","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=280987"},"modified":"2025-08-05T10:05:24","modified_gmt":"2025-08-05T10:05:24","slug":"find-the-area-of-the-triangle-qrs","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/08\/05\/find-the-area-of-the-triangle-qrs\/","title":{"rendered":"Find the area of the triangle QRS."},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/08\/image-517.png\" alt=\"\" class=\"wp-image-280988\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The correct answer is&nbsp;<strong>140<\/strong>&nbsp;square units.<\/p>\n\n\n\n<p>A straightforward way to determine the area of a triangle on a coordinate plane is to use the &#8220;box method.&#8221; This technique involves enclosing the triangle within a rectangle and then subtracting the areas of the smaller right triangles created in the corners.<\/p>\n\n\n\n<p>First, we define the dimensions of the bounding rectangle. We find the minimum and maximum x and y coordinates from the vertices Q(-9, 5), R(6, 10), and S(2, -10). The x-coordinates range from -9 to 6, giving the rectangle a width of 15 units. The y-coordinates range from -10 to 10, giving the rectangle a height of 20 units. The area of this large rectangle is its width times its height, which is 15 multiplied by 20, for a total of 300 square units.<\/p>\n\n\n\n<p>Next, we calculate the areas of the three right triangles that are inside the rectangle but outside of triangle QRS.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>The top triangle has vertices at (-9, 5), (6, 5), and (6, 10). Its base is 15 units and its height is 5 units. Its area is (1\/2) * 15 * 5 = 37.5 square units.<\/li>\n\n\n\n<li>The bottom-right triangle has vertices at (6, 10), (2, -10), and (6, -10). Its base is 4 units and its height is 20 units. Its area is (1\/2) * 4 * 20 = 40 square units.<\/li>\n\n\n\n<li>The bottom-left triangle has vertices at (-9, 5), (2, -10), and (-9, -10). Its base is 11 units and its height is 15 units. Its area is (1\/2) * 11 * 15 = 82.5 square units.<\/li>\n<\/ol>\n\n\n\n<p>Finally, we subtract the sum of these three areas from the total area of the rectangle. The combined area of the corner triangles is 37.5 + 40 + 82.5 = 160 square units. Subtracting this from the rectangle&#8217;s area gives the area of triangle QRS: 300 &#8211; 160 = 140 square units.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/08\/learnexams-banner6-78.jpeg\" alt=\"\" class=\"wp-image-280989\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The Correct Answer and Explanation is: The correct answer is&nbsp;140&nbsp;square units. A straightforward way to determine the area of a triangle on a coordinate plane is to use the &#8220;box method.&#8221; This technique involves enclosing the triangle within a rectangle and then subtracting the areas of the smaller right triangles created in the corners. First, [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-280987","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/280987","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=280987"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/280987\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=280987"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=280987"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=280987"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}