{"id":264,"date":"2017-08-23T04:34:40","date_gmt":"2017-08-23T04:34:40","guid":{"rendered":"http:\/\/americanboard.org\/Subjects\/elementary-education\/?page_id=264"},"modified":"2017-09-25T21:19:08","modified_gmt":"2017-09-25T21:19:08","slug":"measuring-quadrilaterals","status":"publish","type":"page","link":"https:\/\/americanboard.org\/Subjects\/elementary-education\/measuring-quadrilaterals\/","title":{"rendered":"Measuring Quadrilaterals"},"content":{"rendered":"<div class=\"twelve columns\" style=\"margin-top: 10%;\">\n<div class=\"advance\"><a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/measuring-triangles\">\u2b05 Previous Lesson<\/a>\u00a0<a class=\"button\" href=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/geometry-measurement\">Workshop Index<\/a>\u00a0<a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/measuring-circles\">Next Lesson \u27a1<\/a><\/div>\n<p><!-- CONTENT BEGINS HERE --><\/p>\n<h1 id=\"title\">Measuring Quadrilaterals<\/h1>\n<h4>Objective<\/h4>\n<p>In the upcoming section, we\u2019ll review a variety of formulas to measure the perimeter and area of quadrilaterals.<\/p>\n<h4>Previously Covered<\/h4>\n<ul>\n<li>A quadrilateral is a four-sided polygon.<\/li>\n<li>A parallelogram is a quadrilateral whose opposite sides are parallel.<\/li>\n<li>A rectangle is a parallelogram with four right angles.<\/li>\n<li>A rhombus is a parallelogram whose sides are all congruent.<\/li>\n<li>A square is both a rhombus and a rectangle.<\/li>\n<li>A trapezoid is a quadrilateral with exactly one pair of parallel sides.<\/li>\n<\/ul>\n<section>\n<h3>Quadrilaterals: Perimeter<\/h3>\n<p>Recall that the perimeter of a polygon is the sum of the lengths of its sides. Questions involving the perimeter of a parallelogram may rely on your knowledge of the properties of that parallelogram. Let\u2019s look at some examples.<\/p>\n<section class=\"question\">\n<h4>Question<\/h4>\n<p>Which of the following gives the perimeter of a rhombus with side length s?<\/p>\n<ol>\n<li>P = s<sup>2<\/sup><\/li>\n<li>P = 2s<sup>2<\/sup><\/li>\n<li>P = 4s<\/li>\n<li>P = 4s<sup>2<\/sup><\/li>\n<\/ol>\n<p><a class=\"q-answer button button-primary\">Reveal Answer<\/a><\/p>\n<p class=\"q-reveal\">Choice C is the correct answer. The perimeter of a polygon is the sum of the lengths of its sides. Since all four sides of a rhombus are congruent, the perimeter is s + s + s + s, or 4s. In fact, you could have eliminated all of the other choices, since they give measures in square units.<\/p>\n<\/section>\n<section class=\"question\">\n<h4>Question<\/h4>\n<p>Which of the following gives the perimeter of a rectangle with length l and width w?<\/p>\n<ol>\n<li>P = 2lw<\/li>\n<li>P = 4(lw)<\/li>\n<li>P = 2(l + w)<\/li>\n<li>P = 4(l + w)<\/li>\n<\/ol>\n<p><a class=\"q-answer button button-primary\">Reveal Answer<\/a><\/p>\n<p class=\"q-reveal\">Choice C is the correct answer. Since the opposite sides of a rectangle are congruent, they have the same measure. So the perimeter of a rectangle is equal to the sum of 2 lengths (2l) and 2 widths (2w): 2l + 2w = 2(l + w).<\/p>\n<\/section>\n<h3>Quadrilaterals: Area<\/h3>\n<p>Parallelograms: The area of a parallelogram is given by the formula A = bh, where b is the base and h is the height. Again, be careful. Don\u2019t forget that the base and the height must be perpendicular.<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/wp-content\/uploads\/sites\/4\/2017\/08\/bhparallelogram.jpg\" alt=\"Parallelogram\" \/><\/center>Looking Back: Do you now see why the area of a triangle is <img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/wp-content\/uploads\/sites\/4\/2017\/08\/s12_p3_aequalshalf.gif\" alt=\"A= 1\/2bh\" \/>?<\/p>\n<section class=\"question\">\n<h4>Question<\/h4>\n<p>What is the area of this parallelogram?<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/wp-content\/uploads\/sites\/4\/2017\/08\/areaquestion2.jpg\" alt=\"Parallelogram area question\" \/><\/center><\/p>\n<ol>\n<li>4 cm<sup>2<\/sup><\/li>\n<li>8 cm<sup>2<\/sup><\/li>\n<li>9 cm<sup>2<\/sup><\/li>\n<li>14 cm<sup>2<\/sup><\/li>\n<\/ol>\n<p><a class=\"q-answer button button-primary\">Reveal Answer<\/a><\/p>\n<p class=\"q-reveal\">Choice B is correct. The area of a parallelogram is , where b is the base and h is the height. The base of this parallelogram is 4 cm long. Because the height must be perpendicular to the base, the height is 2 cm. If you answered A, you may have used the formula for the area of a triangle rather than the area of a parallelogram. If you answered D, you may have been finding the perimeter rather than the area. So the area is:<\/p>\n<p class=\"q-reveal center\"><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/wp-content\/uploads\/sites\/4\/2017\/08\/6_3a_s12_p4_answer.gif\" alt=\"Answer equation\" \/><\/p>\n<\/section>\n<h3>Trapezoids<\/h3>\n<p>The area of a trapezoid is given by the formula <img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/wp-content\/uploads\/sites\/4\/2017\/08\/6_3a_s12_p4_equation.gif\" alt=\"Formula for area of trapezoid\" \/>, where h is the height and b<sub>1<\/sub> and b<sub>2<\/sub> are the lengths of the parallel bases.<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/wp-content\/uploads\/sites\/4\/2017\/08\/areaoftrapezoid.jpg\" alt=\"Area of a trapezoid\" \/><\/center><\/p>\n<section class=\"question\">\n<h4>Question<\/h4>\n<p>What is the area of the trapezoid below? Round your answer to the nearest tenth of a square centimeter.<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/wp-content\/uploads\/sites\/4\/2017\/08\/areaoftrapezoidquestion.jpg\" alt=\"Trapezoid area question\" \/><\/center><\/p>\n<ol>\n<li>12 cm<sup>2<\/sup><\/li>\n<li>13.5 cm<sup>2<\/sup><\/li>\n<li>27 cm<sup>2<\/sup><\/li>\n<li>30.5 cm<sup>2<\/sup><\/li>\n<\/ol>\n<p><a class=\"q-answer button button-primary\">Reveal Answer<\/a><\/p>\n<p class=\"q-reveal\">Choice B is the correct answer. The area of the trapezoid is given by the formula <img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/wp-content\/uploads\/sites\/4\/2017\/08\/6_3a_s12_p4_equation.gif\" alt=\"Formula for area of trapezoid\" \/>, where h = 3 cm, b<sub>1<\/sub> = 4 cm, and b<sub>2<\/sub> = 5 cm. So the area of the trapezoid is:<br \/>\n<img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/wp-content\/uploads\/sites\/4\/2017\/08\/s12_p4_equation_answer.gif\" alt=\"Answer equation\" \/><\/p>\n<\/section>\n<h3>Review<\/h3>\n<ul>\n<li>The perimeter of a quadrilateral is the sum of the lengths of its sides.<\/li>\n<li>The area of a parallelogram is given by the formula, A= bh where b is the base and h is the height and the base and height are perpendicular.<\/li>\n<li>The area of a trapezoid is given by the formula <img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/wp-content\/uploads\/sites\/4\/2017\/08\/6_3a_s12_p4_equation.gif\" alt=\"Formula for area of trapezoid\" \/>, where h is the height and b1 and b2 are the lengths of the parallel bases.<\/li>\n<\/ul>\n<\/section>\n<p><!-- CONTENT ENDS HERE --><\/p>\n<div class=\"advance\"><a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/measuring-triangles\">\u2b05 Previous Lesson<\/a>\u00a0<a class=\"button\" href=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/geometry-measurement\">Workshop Index<\/a>\u00a0<a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/measuring-circles\">Next Lesson \u27a1<\/a><\/div>\n<p><a class=\"backtotop\" href=\"#title\">Back to Top<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u2b05 Previous Lesson\u00a0Workshop Index\u00a0Next Lesson \u27a1 Measuring Quadrilaterals Objective In the upcoming section, we\u2019ll review a variety of formulas to measure the perimeter and area of quadrilaterals. Previously Covered A quadrilateral is a four-sided polygon. A parallelogram is a quadrilateral whose opposite sides are parallel. A rectangle is a parallelogram with four right angles. A [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-264","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/americanboard.org\/Subjects\/elementary-education\/wp-json\/wp\/v2\/pages\/264","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/americanboard.org\/Subjects\/elementary-education\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/americanboard.org\/Subjects\/elementary-education\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/americanboard.org\/Subjects\/elementary-education\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/americanboard.org\/Subjects\/elementary-education\/wp-json\/wp\/v2\/comments?post=264"}],"version-history":[{"count":8,"href":"https:\/\/americanboard.org\/Subjects\/elementary-education\/wp-json\/wp\/v2\/pages\/264\/revisions"}],"predecessor-version":[{"id":1396,"href":"https:\/\/americanboard.org\/Subjects\/elementary-education\/wp-json\/wp\/v2\/pages\/264\/revisions\/1396"}],"wp:attachment":[{"href":"https:\/\/americanboard.org\/Subjects\/elementary-education\/wp-json\/wp\/v2\/media?parent=264"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}