Area of a Trapezium<\/h3>\n
The trapezium area is the region covered by the trapezium in a two-dimensional plane. It can be measured by taking the average of two bases and multiplied the result by altitude. Therefore, the area of the trapezium formula is given as,<\/p>\n
Trapezium Area A = h(a + b)\/2 square units<\/p>\n
Where,<\/p>\n
a, b are the bases<\/p>\n
h is the height or altitude<\/p>\n
Area of an isosceles Trapezium = 1\/2 [\u221a(c\u00b2 \u2013 (a \u2013 b)\u00b2) (a + b)]<\/p>\n
Where,<\/p>\n
a = AB, b = CD, c = AD<\/p>\n
The perimeter of trapezium P = a + b + c + d units<\/p>\n
Perimeter of the Isosceles Trapezium = a + b + 2c units<\/p>\n
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Prove that:<\/strong><\/p>\n Area of trapezium ABCD = 1\/2[AD + BC] h<\/p>\n Area of trapezium ABCD = area (\u2206DFA) + area (rectangle DFEC) + area (\u2206CEB)<\/p>\n = (\u00b9\/\u2082 \u00d7 AF \u00d7 DF) + (FE \u00d7 DF) + (\u00b9\/\u2082 \u00d7 EB \u00d7 CE)<\/p>\n = (\u00b9\/\u2082 \u00d7 AF \u00d7 h) + (FE \u00d7 h) + (\u00b9\/\u2082 \u00d7 EB \u00d7 h)<\/p>\n = h\/2 x (AF + FE + EB)<\/p>\n = h\/2 \u00d7 (AB + FE)<\/p>\n = h\/2 x (AB + DC)<\/p>\n = \u00b9\/\u2082 \u00d7 (sum of parallel sides) \u00d7 (distance between them)<\/p>\n Therefore, The area of a trapezium = \u00b9\/\u2082 \u00d7 (sum of parallel sides) \u00d7 (distance between them)<\/p>\n Follow the steps to calculate the Area of the Trapezium by referring to the below steps. They are as such<\/p>\n Example 1.<\/strong><\/p>\n In a trapezium, the measurement of one parallel side two more than the other parallel side and the height is 6 cm. The area of the trapezium is 216 cm\u00b2. Find the lengths of the two parallel sides?<\/p>\n Solution:<\/strong><\/p>\n Let a, b are the parallel sides of the trapezium.<\/p>\n According to the question,<\/p>\n One parallel side is two more than the other parallel side<\/p>\n a = b + 2<\/p>\n Area of the trapezium = 216 cm\u00b2<\/p>\n \u00bd(a + b)h = 216<\/p>\n Substitute a = b + 2, h = 6 cm in above equation.<\/p>\n \u00bd(b + 2 + b)4 = 216<\/p>\n 2(2b + 2) = 216<\/p>\n 2b + 2 = 216\/2<\/p>\n 2b + 2 = 108<\/p>\n 2b = 108 \u2013 2<\/p>\n 2b = 106<\/p>\n b = 106\/2<\/p>\n b = 53<\/p>\n Put b = 53 in a = b + 2<\/p>\n a = 53 + 2 = 55<\/p>\n So, the lengths of the two parallel sides are 55 cm, 53 cm.<\/p>\n Example 2.<\/strong><\/p>\n The area of a trapezium is 148 cm\u00b2 and its height is 12 cm. If one of the parallel sides is double of the other, find the two parallel sides?<\/p>\n Solution:<\/strong><\/p>\n Given that,<\/p>\n Area of the trapezium = 148 cm\u00b2<\/p>\n Height = 12 cm<\/p>\n Let one side of the trapezium is a, then another parallel side is b.<\/p>\n As per the question,<\/p>\n One of the parallel sides is double of the other.<\/p>\n a = 2b<\/p>\n Area of the trapezium = 148 cm\u00b2<\/p>\n \u00bd(a + b)h = 148<\/p>\n Substitute a = 2b, h = 12 in above equation.<\/p>\n \u00bd(2b + b) x 12 = 148<\/p>\n 3b x 6 = 148<\/p>\n 18b = 148<\/p>\n b = 148\/18<\/p>\n b = 8.2<\/p>\n Put b = 8.2 in a = 2b<\/p>\n a = 8.2 x 2<\/p>\n a = 16.4<\/p>\n Therefore, the two parallel sides of length are 16.4 cm, 8.2 cm.<\/p>\n Example 3.<\/strong><\/p>\n Find the area of a trapezium whose parallel sides are AB = 42 cm, CD = 16 cm, and non parallel side AD = 15 cm, BC = 15 cm?<\/p>\n Solution:<\/strong><\/p>\n In trapezium ABCD,<\/p>\n CE = 15 cm<\/p>\n CD = 16 cm, AE = 16 cm<\/p>\n EB = AB \u2013 AE = 42 \u2013 16 = 26 cm<\/p>\n Now, in \u2206 EBC<\/p>\n S = (15 + 15 + 26)\/2<\/p>\n S = 56\/2 = 28<\/p>\n Area of triangle = \u221a(s(s \u2013 a) (s \u2013 b) (s \u2013 c))<\/p>\n = \u221a(28 (28 \u2013 15) (28 \u2013 15) (28 \u2013 26))<\/p>\n = \u221a(28 (13) (13) (2))<\/p>\n = \u221a(9464) = 97.2 cm\u00b2<\/p>\n Area of \u2206EBC = 1\/2 \u00d7 EB \u00d7 CP<\/p>\n 97.2 = 1\/2 \u00d7 26 \u00d7 CP<\/p>\n CP x 13 = 97.2<\/p>\n CP = 97.2\/13 = 7.48 cm<\/p>\n Therefore, h = 7.48 cm<\/p>\n Area of trapezium = 1\/2(p\u2081 + p\u2082) \u00d7 h<\/p>\n = 1\/2(58) \u00d7 7.48<\/p>\n = 29 x 7.48 = 216.92 cm\u00b2<\/p>\n Therefore, area of a trapezium is 216.92 cm\u00b2.<\/p>\n Example 4.<\/strong><\/p>\n The length of the parallel sides of a trapezium is in the ratio 5: 8 and the distance between them is 18 cm. If the area of the trapezium is 256 cm\u00b2, find the length of the parallel sides?<\/p>\n Solution:<\/strong><\/p>\n Given that,<\/p>\n The ratio of parallel sides of the trapezium is 5: 8.<\/p>\n The distance between parallel sides = 18 cm<\/p>\n Area of the trapezium = 256 cm\u00b2<\/p>\n Let the common ratio be x,<\/p>\n Then, parallel sides are 5x, 8x.<\/p>\n Area of trapezium = 1\/2 (p\u2081 + p\u2082) h<\/p>\n 256 = 1\/2 (5x + 8x) x 18<\/p>\n 256 = 9(13x)<\/p>\n 256 = 117x<\/p>\n x = 256\/117<\/p>\n x = 2.188<\/p>\n 5x = 5 x 2.188 = 10.94, 8x = 8 x 2.188 = 17.5<\/p>\n Therefore, the length of parallel sides area are 10.94 cm and 17.5 cm.<\/p>\n 1. What is the formula for the Area of a trapezium?<\/p>\n Area of trapezium = \u00bd x Sum of parallel sides x Distance between the parallel sides<\/p>\n Trapezium area = \u00bd x (a+b) x h<\/p>\n 2. What are the applications of a trapezium?<\/p>\n It is used in various physics computations and mathematical calculations.<\/p>\n 3. What are the properties of Trapezium? The trapezium is a quadrilateral that has four sides and one set of parallel sides. The area of trapezium is the region covered by the solid in a two-dimensional plane. Other types of quadrilaterals are parallelogram, rectangle, square, and rhombus. Find the definition, formula, and solved examples on the trapezium area. Trapezium Definition The trapezium … Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/35604"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=35604"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/35604\/revisions"}],"predecessor-version":[{"id":92625,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/35604\/revisions\/92625"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=35604"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=35604"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=35604"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}How to find the Trapezium Area?<\/h3>\n
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Area of a Trapezium Questions and Answers<\/h3>\n
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<\/p>\nFAQs on Area of a Trapezium<\/h3>\n
\nThe trapezium has 4 unequal sides, 2 are parallel and 2 are nonparallel. The sum of the interior angles is 360 degrees and diagonals bisect each other.<\/p>\n","protected":false},"excerpt":{"rendered":"