{"id":235533,"date":"2025-06-15T12:59:25","date_gmt":"2025-06-15T12:59:25","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=235533"},"modified":"2025-06-15T12:59:27","modified_gmt":"2025-06-15T12:59:27","slug":"find-the-perimeter-of-quadrilateral-abcd","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/15\/find-the-perimeter-of-quadrilateral-abcd\/","title":{"rendered":"Find the perimeter of quadrilateral ABCD"},"content":{"rendered":"\n

Find the perimeter of quadrilateral ABCD. Round to the nearest tenth. A 5 4 3 B D 2 1 1 2 3 4 5 -1 C 11.3 units 14.6 units 17.4 units 56.0 units<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

ChatGPT said:<\/h6>\n\n\n\n

To find the perimeter of quadrilateral ABCDABCDABCD, the distance between each pair of adjacent vertices must be calculated using the distance formula:Distance=(x2\u2212x1)2+(y2\u2212y1)2\\text{Distance} = \\sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}Distance=(x2\u200b\u2212x1\u200b)2+(y2\u200b\u2212y1\u200b)2\u200b<\/p>\n\n\n\n

Coordinates of the points from the image:<\/p>\n\n\n\n

    \n
  • A(3,5)A(3, 5)A(3,5)<\/li>\n\n\n\n
  • B(1,3)B(1, 3)B(1,3)<\/li>\n\n\n\n
  • C(3,0)C(3, 0)C(3,0)<\/li>\n\n\n\n
  • D(5,3)D(5, 3)D(5,3)<\/li>\n<\/ul>\n\n\n\n

    Step 1: Calculate the distance AB<\/h3>\n\n\n\n

    AB=(3\u22121)2+(5\u22123)2=22+22=4+4=8\u22482.8AB = \\sqrt{(3 – 1)^2 + (5 – 3)^2} = \\sqrt{2^2 + 2^2} = \\sqrt{4 + 4} = \\sqrt{8} \\approx 2.8AB=(3\u22121)2+(5\u22123)2\u200b=22+22\u200b=4+4\u200b=8\u200b\u22482.8<\/p>\n\n\n\n

    Step 2: Calculate the distance BC<\/h3>\n\n\n\n

    BC=(3\u22121)2+(0\u22123)2=22+(\u22123)2=4+9=13\u22483.6BC = \\sqrt{(3 – 1)^2 + (0 – 3)^2} = \\sqrt{2^2 + (-3)^2} = \\sqrt{4 + 9} = \\sqrt{13} \\approx 3.6BC=(3\u22121)2+(0\u22123)2\u200b=22+(\u22123)2\u200b=4+9\u200b=13\u200b\u22483.6<\/p>\n\n\n\n

    Step 3: Calculate the distance CD<\/h3>\n\n\n\n

    CD=(5\u22123)2+(3\u22120)2=22+32=4+9=13\u22483.6CD = \\sqrt{(5 – 3)^2 + (3 – 0)^2} = \\sqrt{2^2 + 3^2} = \\sqrt{4 + 9} = \\sqrt{13} \\approx 3.6CD=(5\u22123)2+(3\u22120)2\u200b=22+32\u200b=4+9\u200b=13\u200b\u22483.6<\/p>\n\n\n\n

    Step 4: Calculate the distance DA<\/h3>\n\n\n\n

    DA=(5\u22123)2+(3\u22125)2=22+(\u22122)2=4+4=8\u22482.8DA = \\sqrt{(5 – 3)^2 + (3 – 5)^2} = \\sqrt{2^2 + (-2)^2} = \\sqrt{4 + 4} = \\sqrt{8} \\approx 2.8DA=(5\u22123)2+(3\u22125)2\u200b=22+(\u22122)2\u200b=4+4\u200b=8\u200b\u22482.8<\/p>\n\n\n\n

    Step 5: Add all sides to find the perimeter<\/h3>\n\n\n\n

    Perimeter\u22482.8+3.6+3.6+2.8=12.8\\text{Perimeter} \\approx 2.8 + 3.6 + 3.6 + 2.8 = 12.8Perimeter\u22482.8+3.6+3.6+2.8=12.8<\/p>\n\n\n\n

    Upon re-checking the diagram and actual coordinates:<\/p>\n\n\n\n

      \n
    • AB=(3\u22121)2+(5\u22123)2=8\u22482.8AB = \\sqrt{(3 – 1)^2 + (5 – 3)^2} = \\sqrt{8} \\approx 2.8AB=(3\u22121)2+(5\u22123)2\u200b=8\u200b\u22482.8<\/li>\n\n\n\n
    • BC=(3\u22121)2+(0\u22123)2=13\u22483.6BC = \\sqrt{(3 – 1)^2 + (0 – 3)^2} = \\sqrt{13} \\approx 3.6BC=(3\u22121)2+(0\u22123)2\u200b=13\u200b\u22483.6<\/li>\n\n\n\n
    • CD=(5\u22123)2+(3\u22120)2=13\u22483.6CD = \\sqrt{(5 – 3)^2 + (3 – 0)^2} = \\sqrt{13} \\approx 3.6CD=(5\u22123)2+(3\u22120)2\u200b=13\u200b\u22483.6<\/li>\n\n\n\n
    • DA=(5\u22123)2+(3\u22125)2=8\u22482.8DA = \\sqrt{(5 – 3)^2 + (3 – 5)^2} = \\sqrt{8} \\approx 2.8DA=(5\u22123)2+(3\u22125)2\u200b=8\u200b\u22482.8<\/li>\n<\/ul>\n\n\n\n

      Total perimeter=2.8+3.6+3.6+2.8=12.8\u2009units\\text{Total perimeter} = 2.8 + 3.6 + 3.6 + 2.8 = 12.8 \\, \\text{units}Total perimeter=2.8+3.6+3.6+2.8=12.8units<\/p>\n\n\n\n

      This does not match any choices. Let’s re-calculate more precisely:<\/p>\n\n\n\n

        \n
      • AB=(3\u22121)2+(5\u22123)2=4+4=8\u22482.83AB = \\sqrt{(3-1)^2 + (5-3)^2} = \\sqrt{4 + 4} = \\sqrt{8} \\approx 2.83AB=(3\u22121)2+(5\u22123)2\u200b=4+4\u200b=8\u200b\u22482.83<\/li>\n\n\n\n
      • BC=(3\u22121)2+(0\u22123)2=4+9=13\u22483.61BC = \\sqrt{(3-1)^2 + (0-3)^2} = \\sqrt{4 + 9} = \\sqrt{13} \\approx 3.61BC=(3\u22121)2+(0\u22123)2\u200b=4+9\u200b=13\u200b\u22483.61<\/li>\n\n\n\n
      • CD=(5\u22123)2+(3\u22120)2=4+9=13\u22483.61CD = \\sqrt{(5-3)^2 + (3-0)^2} = \\sqrt{4 + 9} = \\sqrt{13} \\approx 3.61CD=(5\u22123)2+(3\u22120)2\u200b=4+9\u200b=13\u200b\u22483.61<\/li>\n\n\n\n
      • DA=(5\u22123)2+(3\u22125)2=4+4=8\u22482.83DA = \\sqrt{(5-3)^2 + (3-5)^2} = \\sqrt{4 + 4} = \\sqrt{8} \\approx 2.83DA=(5\u22123)2+(3\u22125)2\u200b=4+4\u200b=8\u200b\u22482.83<\/li>\n<\/ul>\n\n\n\n

        Total=2.83+3.61+3.61+2.83=12.88\u2009units\\text{Total} = 2.83 + 3.61 + 3.61 + 2.83 = 12.88 \\, \\text{units}Total=2.83+3.61+3.61+2.83=12.88units<\/p>\n\n\n\n

        Still not matching the given choices. However, a more accurate interpretation of the image reveals:<\/p>\n\n\n\n

          \n
        • AB=(3\u22121)2+(5\u22123)2=4+4=8\u22482.8AB = \\sqrt{(3 – 1)^2 + (5 – 3)^2} = \\sqrt{4 + 4} = \\sqrt{8} \u2248 2.8AB=(3\u22121)2+(5\u22123)2\u200b=4+4\u200b=8\u200b\u22482.8<\/li>\n\n\n\n
        • BC=(3\u22121)2+(0\u22123)2=4+9=13\u22483.6BC = \\sqrt{(3 – 1)^2 + (0 – 3)^2} = \\sqrt{4 + 9} = \\sqrt{13} \u2248 3.6BC=(3\u22121)2+(0\u22123)2\u200b=4+9\u200b=13\u200b\u22483.6<\/li>\n\n\n\n
        • CD=(5\u22123)2+(3\u22120)2=4+9=13\u22483.6CD = \\sqrt{(5 – 3)^2 + (3 – 0)^2} = \\sqrt{4 + 9} = \\sqrt{13} \u2248 3.6CD=(5\u22123)2+(3\u22120)2\u200b=4+9\u200b=13\u200b\u22483.6<\/li>\n\n\n\n
        • DA=(5\u22123)2+(3\u22125)2=4+4=8\u22482.8DA = \\sqrt{(5 – 3)^2 + (3 – 5)^2} = \\sqrt{4 + 4} = \\sqrt{8} \u2248 2.8DA=(5\u22123)2+(3\u22125)2\u200b=4+4\u200b=8\u200b\u22482.8<\/li>\n<\/ul>\n\n\n\n

          Sum: 2.8+3.6+3.6+2.8=12.82.8 + 3.6 + 3.6 + 2.8 = 12.82.8+3.6+3.6+2.8=12.8<\/p>\n\n\n\n

          Wait \u2014 the correct coordinates from the graph are:<\/p>\n\n\n\n

            \n
          • A: (3, 5)<\/li>\n\n\n\n
          • B: (1, 3)<\/li>\n\n\n\n
          • C: (3, -1)<\/li>\n\n\n\n
          • D: (5, 3)<\/li>\n<\/ul>\n\n\n\n

            Now using these:<\/p>\n\n\n\n

              \n
            • AB: (3\u22121)2+(5\u22123)2=4+4=8\u22482.8\\sqrt{(3 – 1)^2 + (5 – 3)^2} = \\sqrt{4 + 4} = \\sqrt{8} \u2248 2.8(3\u22121)2+(5\u22123)2\u200b=4+4\u200b=8\u200b\u22482.8<\/li>\n\n\n\n
            • BC: (3\u22121)2+(\u22121\u22123)2=4+16=20\u22484.5\\sqrt{(3 – 1)^2 + (-1 – 3)^2} = \\sqrt{4 + 16} = \\sqrt{20} \u2248 4.5(3\u22121)2+(\u22121\u22123)2\u200b=4+16\u200b=20\u200b\u22484.5<\/li>\n\n\n\n
            • CD: (5\u22123)2+(3\u2212(\u22121))2=4+16=20\u22484.5\\sqrt{(5 – 3)^2 + (3 – (-1))^2} = \\sqrt{4 + 16} = \\sqrt{20} \u2248 4.5(5\u22123)2+(3\u2212(\u22121))2\u200b=4+16\u200b=20\u200b\u22484.5<\/li>\n\n\n\n
            • DA: (5\u22123)2+(3\u22125)2=4+4=8\u22482.8\\sqrt{(5 – 3)^2 + (3 – 5)^2} = \\sqrt{4 + 4} = \\sqrt{8} \u2248 2.8(5\u22123)2+(3\u22125)2\u200b=4+4\u200b=8\u200b\u22482.8<\/li>\n<\/ul>\n\n\n\n

              Now:2.8+4.5+4.5+2.8=14.6\u2009units2.8 + 4.5 + 4.5 + 2.8 = 14.6 \\, \\text{units}2.8+4.5+4.5+2.8=14.6units<\/p>\n\n\n\n

              \u2705 Correct answer: 14.6 units<\/strong>.<\/p>\n\n\n\n

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

              Find the perimeter of quadrilateral ABCD. Round to the nearest tenth. A 5 4 3 B D 2 1 1 2 3 4 5 -1 C 11.3 units 14.6 units 17.4 units 56.0 units The Correct Answer and Explanation is: ChatGPT said: To find the perimeter of quadrilateral ABCDABCDABCD, the distance between each pair of […]<\/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-235533","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/235533","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=235533"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/235533\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=235533"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=235533"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=235533"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}