{"id":277834,"date":"2025-08-01T15:54:17","date_gmt":"2025-08-01T15:54:17","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=277834"},"modified":"2025-08-01T15:54:19","modified_gmt":"2025-08-01T15:54:19","slug":"what-is-the-perimeter-of-polygon-lmnpq","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/08\/01\/what-is-the-perimeter-of-polygon-lmnpq\/","title":{"rendered":"What is the perimeter of polygon LMNPQ"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The correct perimeter of the polygon LMNPQ is 12 + 4\u221a2<\/strong> units, which is approximately 17.66 units<\/strong>.<\/p>\n\n\n\n

To find the perimeter of the polygon, we must calculate the length of each of its five sides and then add these lengths together. The polygon is on a coordinate plane, so we can determine the coordinates of each vertex first: L is at (4, 2), M is at (2, 4), N is at (5, 8), P is at (8, 4), and Q is at (6, 2).<\/p>\n\n\n\n

We use the distance formula, d = \u221a((x\u2082 – x\u2081)\u00b2 + (y\u2082 – y\u2081)\u00b2), to find the length of each segment.<\/p>\n\n\n\n

    \n
  1. Length of QL:<\/strong>\u00a0This is a horizontal segment. We can find its length by subtracting the x-coordinates: |6 – 4| = 2 units.<\/li>\n\n\n\n
  2. Length of LM:<\/strong>\u00a0Using the coordinates for L(4, 2) and M(2, 4):
    d = \u221a((2 – 4)\u00b2 + (4 – 2)\u00b2) = \u221a((-2)\u00b2 + 2\u00b2) = \u221a(4 + 4) = \u221a8 units.<\/li>\n\n\n\n
  3. Length of MN:<\/strong>\u00a0Using the coordinates for M(2, 4) and N(5, 8):
    d = \u221a((5 – 2)\u00b2 + (8 – 4)\u00b2) = \u221a(3\u00b2 + 4\u00b2) = \u221a(9 + 16) = \u221a25 = 5 units.<\/li>\n\n\n\n
  4. Length of NP:<\/strong>\u00a0Using the coordinates for N(5, 8) and P(8, 4):
    d = \u221a((8 – 5)\u00b2 + (4 – 8)\u00b2) = \u221a(3\u00b2 + (-4)\u00b2) = \u221a(9 + 16) = \u221a25 = 5 units.<\/li>\n\n\n\n
  5. Length of PQ:<\/strong>\u00a0Using the coordinates for P(8, 4) and Q(6, 2):
    d = \u221a((6 – 8)\u00b2 + (2 – 4)\u00b2) = \u221a((-2)\u00b2 + (-2)\u00b2) = \u221a(4 + 4) = \u221a8 units.<\/li>\n<\/ol>\n\n\n\n

    Finally, we sum the lengths of all the sides to get the total perimeter:
    Perimeter = QL + LM + MN + NP + PQ
    Perimeter = 2 + \u221a8 + 5 + 5 + \u221a8
    Perimeter = 12 + 2\u221a8<\/p>\n\n\n\n

    To simplify, we can write \u221a8 as \u221a(4 * 2), which is 2\u221a2.
    Perimeter = 12 + 2(2\u221a2) = 12 + 4\u221a2 units.
    Using a calculator, \u221a2 is approximately 1.414, so the perimeter is about 12 + 4(1.414) = 12 + 5.656 = 17.656, which rounds to 17.66 units.<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    The correct answer and explanation is: The correct perimeter of the polygon LMNPQ is 12 + 4\u221a2 units, which is approximately 17.66 units. To find the perimeter of the polygon, we must calculate the length of each of its five sides and then add these lengths together. The polygon is on a coordinate plane, so we can determine […]<\/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-277834","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/277834","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=277834"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/277834\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=277834"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=277834"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=277834"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}