{"id":2714,"date":"2023-05-01T10:00:10","date_gmt":"2023-05-01T04:30:10","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=2714"},"modified":"2023-05-02T10:18:01","modified_gmt":"2023-05-02T04:48:01","slug":"area-of-trapezium","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/area-of-trapezium\/","title":{"rendered":"How To Find Area Of Trapezium"},"content":{"rendered":"<h2><strong>Area Of Trapezium Example Problems With Solutions<\/strong><\/h2>\n<p><strong>Trapezium<\/strong> &#8211; A quadrilateral which has one pair of opposite sides parallel.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-12829 aligncenter\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/area-of-trapezium-1.jpg\" alt=\"\" width=\"390\" height=\"233\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/area-of-trapezium-1.jpg 390w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/area-of-trapezium-1-300x179.jpg 300w\" sizes=\"(max-width: 390px) 100vw, 390px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-12830 aligncenter\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/area-of-trapezium-2.jpg\" alt=\"\" width=\"547\" height=\"488\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/area-of-trapezium-2.jpg 547w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/area-of-trapezium-2-300x268.jpg 300w\" sizes=\"(max-width: 547px) 100vw, 547px\" \/><\/p>\n<p><iframe loading=\"lazy\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/UYrhj3h35sU?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<p><strong>Example 1:<\/strong> \u00a0 \u00a0Find the area of a trapezium whose parallel sides 25 cm, 13 cm and other sides are 15 cm and 15 cm<br \/>\n<strong>Solution:<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128147\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/04\/How-To-Find-Area-Of-Trapezium-2.png\" alt=\"How To Find Area Of Trapezium 2\" width=\"389\" height=\"243\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/04\/How-To-Find-Area-Of-Trapezium-2.png 389w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/04\/How-To-Find-Area-Of-Trapezium-2-300x187.png 300w\" sizes=\"(max-width: 389px) 100vw, 389px\" \/><br \/>\nIn \u0394CEF,<br \/>\nCE = 10 cm and EF = 6cm<br \/>\nUsing Pythagoras theorem:<br \/>\nCE\u00b2 = CF\u00b2 + EF\u00b2<br \/>\nCF\u00b2 = CE\u00b2 \u2013 EF\u00b2<br \/>\nCF\u00b2 = 15\u00b2 \u2013 6\u00b2<br \/>\nCF\u00b2 = 225-36<br \/>\nCF\u00b2 = 189<br \/>\nCF = \u221a189<br \/>\n= \u221a (9\u00d721)<br \/>\n= 3\u221a21 cm<br \/>\nFrom the figure we can write,<br \/>\nArea of trapezium = Area of parallelogram AECD + Area of area of triangle CEF<br \/>\nArea of trapezium = height + \\(\\frac { 1 }{ 2 } \\) (sum of parallel sides)<br \/>\nArea of trapezium = 3\u221a21 \u00d7 \\(\\frac { 1 }{ 2 } \\) (25 + 13)<br \/>\nArea of trapezium = 3\u221a21 \u00d7 19 = 57\u221a21<br \/>\n\u2234 Area of trapezium = 57\u221a21 cm\u00b2<\/p>\n<p><strong>Example 2: \u00a0\u00a0<\/strong>\u00a0A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The nonparallel sides are 14 m and 13 m. Find the area of the field.<br \/>\n<strong>Solution:<\/strong><br \/>\nLet ABCD be a trapezium with, AB\u2225CD<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128168\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-5.png\" alt=\"How To Find Area Of Trapezium 5\" width=\"366\" height=\"250\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-5.png 366w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-5-300x205.png 300w\" sizes=\"(max-width: 366px) 100vw, 366px\" \/><br \/>\nAB = 25m<br \/>\nCD = 10m<br \/>\nBC = 14m<br \/>\nAD = 13m<br \/>\nDraw CE\u2225DA. So, ADCE is a parallelogram with,<br \/>\nCD = AE = 10m<br \/>\nCE = AD = 13m<br \/>\nBE = AB \u2212 AE = 25 \u2212 10 = 15m<br \/>\nIn \u0394BCE, the semi perimeter will be,<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128160\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-3.png\" alt=\"How To Find Area Of Trapezium 3\" width=\"307\" height=\"286\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-3.png 307w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-3-300x279.png 300w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><br \/>\nAlso, area of \u0394BCE is,<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128166\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-4.png\" alt=\"How To Find Area Of Trapezium 4\" width=\"320\" height=\"331\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-4.png 320w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-4-290x300.png 290w\" sizes=\"(max-width: 320px) 100vw, 320px\" \/><br \/>\nTherefore, the area of the trapezium is 196 m\u00b2<\/p>\n<p><strong>Example 3: \u00a0 \u00a0<\/strong>Students of a school staged a rally for cleanliness compaign. They walked through the lanes in two groups. One group walked through the lanes AB, BC and CA, while other through AC, CD and DA (see fig.). Then they cleaned the area enclosed within their lanes. If AB = 9 m, BC = 40 m, CD = 15 m, DA = 28 m, and \u2220B = 90\u00b0. Which group cleaned more area and by how much? Find the total area cleaned by the students.<br \/>\n<strong>Solution:<\/strong><br \/>\nGiven, \u0394ABC is a right-angled triangle.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128174\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-6.png\" alt=\"How To Find Area Of Trapezium 6\" width=\"357\" height=\"203\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-6.png 357w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-6-300x171.png 300w\" sizes=\"(max-width: 357px) 100vw, 357px\" \/><br \/>\nTherefore, AC\u00b2 = AB\u00b2 + BC\u00b2\u00a0 &#8230; [Using Pythagoras Theorem]<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128176\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-7.png\" alt=\"How To Find Area Of Trapezium 7\" width=\"522\" height=\"418\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-7.png 522w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-7-300x240.png 300w\" sizes=\"(max-width: 522px) 100vw, 522px\" \/><br \/>\nSo, group 1 covered area \u0394ABC=180m\u00b2 and group 2 covered area \u0394DAC = 126m\u00b2<br \/>\nHence, group 1 covers more area by group 2 which is 54m\u00b2 = (180m\u00b2 \u2212 126m\u00b2) more.<br \/>\nNow, area covered by both the groups = Area ABC + Area DAC = 180m\u00b2 + 126m\u00b2 = 306m\u00b2<\/p>\n<p><strong>Example 4: \u00a0 \u00a0<\/strong>Radha made a picture of an aeroplane with coloured paper as shown in figure. Find the total area of the paper used.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128187\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-8.png\" alt=\"How To Find Area Of Trapezium 8\" width=\"388\" height=\"412\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-8.png 388w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-8-283x300.png 283w\" sizes=\"(max-width: 388px) 100vw, 388px\" \/><br \/>\n<strong>Solution:<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128189\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-9.png\" alt=\"How To Find Area Of Trapezium 9\" width=\"406\" height=\"515\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-9.png 406w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-9-237x300.png 237w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128191\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-10.png\" alt=\"How To Find Area Of Trapezium 10\" width=\"318\" height=\"64\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-10.png 318w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-10-300x60.png 300w\" sizes=\"(max-width: 318px) 100vw, 318px\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128193\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-11.png\" alt=\"How To Find Area Of Trapezium 11\" width=\"447\" height=\"515\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-11.png 447w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-11-260x300.png 260w\" sizes=\"(max-width: 447px) 100vw, 447px\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128195\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-12.png\" alt=\"How To Find Area Of Trapezium 12\" width=\"364\" height=\"424\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-12.png 364w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-12-258x300.png 258w\" sizes=\"(max-width: 364px) 100vw, 364px\" \/><br \/>\nArea of Rectangle = Length\u00a0\u00d7 bredth<br \/>\n= 6.5\u00a0\u00d7 1 =6.5 cm\u00b2<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128196\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-13.png\" alt=\"How To Find Area Of Trapezium 13\" width=\"513\" height=\"345\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-13.png 513w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-13-300x202.png 300w\" sizes=\"(max-width: 513px) 100vw, 513px\" \/><br \/>\nHence we have the following<br \/>\nArea of III = Area of I + Area of II + Area of III<br \/>\nI and III are right angled triangles.<br \/>\narea (I) +area (II) = 2 area (I) (By symmetry)<br \/>\n= 2 \u00d7\u00a0\\(\\frac { 1 }{ 2 } \\)\u00a0\u00d7 0.5\u00a0\u00d7 1<br \/>\n= 0.5 cm\u00b2<\/p>\n<p>(II) is a rectangle<br \/>\n\u2234 Area (II) =\u00a0Length\u00a0\u00d7 bredth<br \/>\n= 1\u00a0\u00d7 1 = 1 cm\u00b2<\/p>\n<p>Area of III = Area of I + Area of II + Area of III<br \/>\n= 0.5\u00a0\u00d7 1 = 1.5 cm\u00b2<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128197\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-14.png\" alt=\"How To Find Area Of Trapezium 14\" width=\"456\" height=\"246\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-14.png 456w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-14-300x162.png 300w\" sizes=\"(max-width: 456px) 100vw, 456px\" \/><br \/>\n(IV) and (V) are similar right angled triangles.<br \/>\nArea of (IV) = Area of (V) =\u00a0\\(\\frac { 1 }{ 2 } \\)\u00a0\u00d7 Base\u00a0\u00d7 Height<br \/>\n=\u00a0\\(\\frac { 1 }{ 2 } \\)\u00a0\u00d7 1.5\u00a0\u00d7 6<br \/>\n= 3\u00a0\u00d7 1.5<br \/>\n= 4.5 cm\u00b2<\/p>\n<p>Thus,<br \/>\nArea = Area of I + Area of II + Area of III +\u00a0Area of IV + Area of V<br \/>\n= 2.48 + 6.5 + 1.5 + 4.5 + 4.5<br \/>\n= 2.48 + 8.0 + 9.0<br \/>\n= 17.0 + 2.48<br \/>\n= 19.48 cm\u00b2<br \/>\n= 19.4 cm\u00b2<\/p>\n<p><strong>Example 5: \u00a0 \u00a0<\/strong>An umbrella is made by stitching 10 triangular pieces of cloth of two different colours (see figure), each piece measuring 20 cm, 50 cm and 50 cm. How much cloth of each colour is required for the umbrella?<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128203\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-15.png\" alt=\"How To Find Area Of Trapezium 15\" width=\"190\" height=\"199\" \/><br \/>\n<strong>Solution:<\/strong><br \/>\nThere are 10 triangles, out of which 5 of black and 5 of grey color. Now,<br \/>\nArea of of each cloth = 5 \u00d7 area of 1 triangle<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128204\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-16.png\" alt=\"How To Find Area Of Trapezium 16\" width=\"564\" height=\"186\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-16.png 564w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-16-300x99.png 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><br \/>\nArea of each cloth required = (5 \u00d7 200\u221a6) = 1000\u221a6 cm\u00b2<\/p>\n<p><strong>Example 6: \u00a0 \u00a0<\/strong>A floral design on a floor is made up of 16 tiles which are triangular, the sides of the triangle being 9 cm, 28 cm and 35 cm (see figure). Find the cost of polishing the tiles at the rate of 50 paisa per cm<sup>2<\/sup>.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128206\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-17.png\" alt=\"How To Find Area Of Trapezium 17\" width=\"204\" height=\"163\" \/><br \/>\n<strong>Solution:<\/strong><br \/>\nGiven that<br \/>\na = 35cm, b = 28cm, c = 9cm<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128208\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-18.png\" alt=\"How To Find Area Of Trapezium 18\" width=\"452\" height=\"254\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-18.png 452w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-18-300x169.png 300w\" sizes=\"(max-width: 452px) 100vw, 452px\" \/><br \/>\n= 36 \u00d7 2.45 = 88.2 cm\u00b2<br \/>\nArea of total 16 tiles = 16 \u00d7 88.2 = 1411.2 cm\u00b2<br \/>\nCost of polishing per cm\u00b2 area = 50p<br \/>\nCost of polishing 1411.2 cm\u00b2 area = Rs. 50 \u00d7 1411.2 = Rs. 705.60<\/p>\n<p><strong>Example 7: \u00a0 \u00a0<\/strong>Sanya has a piece of land which is in the shape of a rhombus. She wants her one daughter and one son to work on the land and produce different crops to suffice the needs of their family. She divided the land in two equals parts. If the perimeter of the land is 400 m and one of the diagonals is 160 m, how much area each of them will get ?<br \/>\n<strong>Solution:<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128221\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-19.png\" alt=\"How To Find Area Of Trapezium 19\" width=\"347\" height=\"220\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-19.png 347w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-19-300x190.png 300w\" sizes=\"(max-width: 347px) 100vw, 347px\" \/><\/p>\n<p>Let ABCD be the field. Given perimeter = 400 m<br \/>\nSo, each side = \\(\\frac { 400 }{ 4 } \\) = 100 m<br \/>\nDiagonal BD = 160 m<br \/>\nLet a = 100 m, b = 100 m, c = 160 m<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128222\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-20.png\" alt=\"How To Find Area Of Trapezium 20\" width=\"392\" height=\"67\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-20.png 392w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-20-300x51.png 300w\" sizes=\"(max-width: 392px) 100vw, 392px\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128223\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-21.png\" alt=\"How To Find Area Of Trapezium 21\" width=\"503\" height=\"469\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-21.png 503w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-21-300x280.png 300w\" sizes=\"(max-width: 503px) 100vw, 503px\" \/><br \/>\nHence, each of the two children will get an area of 4800 m<sup>2<\/sup>.<\/p>\n<p><strong>Example 8: \u00a0 \u00a0<\/strong>There is a slide in a park. One of its side walls has been painted in some colour with a message \u2018\u2018KEEP THE PARK GREEN AND CLEAN\u2019\u2019 (see figure). If the sides of the wall are 15 m, 11 m and 6 m, find the area painted in colour.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128226\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-22.png\" alt=\"How To Find Area Of Trapezium 22\" width=\"465\" height=\"170\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-22.png 465w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-22-300x110.png 300w\" sizes=\"(max-width: 465px) 100vw, 465px\" \/><br \/>\n<strong>Solution:<\/strong><br \/>\nGiven that<br \/>\nSides: a = 15m, b = 11m and c = 6m<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128228\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-23.png\" alt=\"How To Find Area Of Trapezium 23\" width=\"334\" height=\"62\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-23.png 334w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-23-300x56.png 300w\" sizes=\"(max-width: 334px) 100vw, 334px\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128229\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-24.png\" alt=\"How To Find Area Of Trapezium 24\" width=\"464\" height=\"437\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-24.png 464w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-24-300x283.png 300w\" sizes=\"(max-width: 464px) 100vw, 464px\" \/><br \/>\n\u2234 The area painted in color is = 20\u221a2 m\u00b2<\/p>\n<p><strong>Example 9: \u00a0 \u00a0<\/strong>A triangular park ABC has sides 120 m, 80 m and 50 m (see fig.). A gardener Dhania has to put a fence all around it and also plant grass inside. How much area does she need to plant? Find the cost of fencing it with barbed wire at the rate of 20 per metre leaving a space 3m wide for a gate on one side.<br \/>\n<strong>Solution: \u00a0 \u00a0<\/strong>Computation of area:<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128232\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-25.png\" alt=\"How To Find Area Of Trapezium 25\" width=\"264\" height=\"122\" \/><br \/>\nClearly, the park is triangular with sides<br \/>\na = BC = 120 m, b = CA = 80 m and<br \/>\nc = AB = 50 m<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128233\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-26.png\" alt=\"How To Find Area Of Trapezium 26\" width=\"447\" height=\"157\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-26.png 447w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-26-300x105.png 300w\" sizes=\"(max-width: 447px) 100vw, 447px\" \/><br \/>\nNumber of meters to be fenced = 50 + 80 + 120 &#8211; 3<br \/>\n= 250 &#8211; 3 = 247 m<br \/>\ncost of fencing = Rs 20 per metre.<br \/>\ncost of fencing park = Rs 20 \u00d7 247<br \/>\n= Rs 4940<\/p>\n<p><strong>Example 10: \u00a0 \u00a0<\/strong>The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 122 m, 22 m and 120 m (see fig.). The advertisements yield an earning of 5000 per m<sup>2<\/sup> per year. A company hired both walls for 3 months. How much rent did it pay ?<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128235\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-27.png\" alt=\"How To Find Area Of Trapezium 27\" width=\"434\" height=\"217\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-27.png 434w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-27-300x150.png 300w\" sizes=\"(max-width: 434px) 100vw, 434px\" \/><br \/>\n<strong>Solution:<\/strong><br \/>\nIn \u0394ABC<br \/>\na = 122m, b = 22m, c = 120m<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128236\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-28.png\" alt=\"How To Find Area Of Trapezium 28\" width=\"604\" height=\"438\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-28.png 604w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-28-300x218.png 300w\" sizes=\"(max-width: 604px) 100vw, 604px\" \/><\/p>\n<p><strong>Example 11: \u00a0 \u00a0<\/strong>Sides of a triangle are in the ratio of 12 : 17 : 25\u00a0 and its perimeter is 540 cm. Find its area.<br \/>\n<strong>Solution:<\/strong><br \/>\nLet x be common ratio<br \/>\n\u2234 Sides of triangle will be: 12x, 17x and 25x<br \/>\nPerimeter = 540 cm(given)<br \/>\n\u21d2 12x + 17x + 25x = 540 cm,<br \/>\n\u21d2 54x = 540 cm<br \/>\n\u21d2 x = 10 cm<br \/>\n\u2234 Sides of triangle: a=120,b=170,c=250 cms<br \/>\n\u21d2 2s = 540<br \/>\n\u21d2 s = 270 cm<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128237\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-29.png\" alt=\"How To Find Area Of Trapezium 29\" width=\"391\" height=\"155\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-29.png 391w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/How-To-Find-Area-Of-Trapezium-29-300x119.png 300w\" sizes=\"(max-width: 391px) 100vw, 391px\" \/><br \/>\n\u2234 A = 9000 cm\u00b2<\/p>\n<p><strong>Example 12: \u00a0 \u00a0<\/strong>Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is<br \/>\n42 cm.<br \/>\n<strong>Solution:<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2721 size-full\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/Area-Of-Trapezium-Example-12.png\" alt=\"area-of-trapezium-example-12\" width=\"434\" height=\"298\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/Area-Of-Trapezium-Example-12.png 434w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/Area-Of-Trapezium-Example-12-300x206.png 300w\" sizes=\"(max-width: 434px) 100vw, 434px\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Area Of Trapezium Example Problems With Solutions Trapezium &#8211; A quadrilateral which has one pair of opposite sides parallel. Example 1: \u00a0 \u00a0Find the area of a trapezium whose parallel sides 25 cm, 13 cm and other sides are 15 cm and 15 cm Solution: In \u0394CEF, CE = 10 cm and EF = 6cm [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[5],"tags":[1161,1162,1163,1164,1154],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.8 (Yoast SEO v17.8) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>How To Find Area Of Trapezium - A Plus Topper<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.aplustopper.com\/area-of-trapezium\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"How To Find Area Of Trapezium\" \/>\n<meta property=\"og:description\" content=\"Area Of Trapezium Example Problems With Solutions Trapezium &#8211; A quadrilateral which has one pair of opposite sides parallel. 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Example 1: \u00a0 \u00a0Find the area of a trapezium whose parallel sides 25 cm, 13 cm and other sides are 15 cm and 15 cm Solution: In \u0394CEF, CE = 10 cm and EF = 6cm [&hellip;]","og_url":"https:\/\/www.aplustopper.com\/area-of-trapezium\/","og_site_name":"A Plus Topper","article_publisher":"https:\/\/www.facebook.com\/aplustopper\/","article_published_time":"2023-05-01T04:30:10+00:00","article_modified_time":"2023-05-02T04:48:01+00:00","og_image":[{"url":"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/area-of-trapezium-1.jpg"}],"twitter_card":"summary","twitter_misc":{"Written by":"Veerendra","Est. reading time":"5 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/www.aplustopper.com\/#organization","name":"Aplus Topper","url":"https:\/\/www.aplustopper.com\/","sameAs":["https:\/\/www.facebook.com\/aplustopper\/"],"logo":{"@type":"ImageObject","@id":"https:\/\/www.aplustopper.com\/#logo","inLanguage":"en-US","url":"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg","contentUrl":"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg","width":1585,"height":375,"caption":"Aplus Topper"},"image":{"@id":"https:\/\/www.aplustopper.com\/#logo"}},{"@type":"WebSite","@id":"https:\/\/www.aplustopper.com\/#website","url":"https:\/\/www.aplustopper.com\/","name":"A Plus Topper","description":"Improve your Grades","publisher":{"@id":"https:\/\/www.aplustopper.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.aplustopper.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"ImageObject","@id":"https:\/\/www.aplustopper.com\/area-of-trapezium\/#primaryimage","inLanguage":"en-US","url":"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/area-of-trapezium-1.jpg","contentUrl":"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/area-of-trapezium-1.jpg","width":390,"height":233},{"@type":"WebPage","@id":"https:\/\/www.aplustopper.com\/area-of-trapezium\/#webpage","url":"https:\/\/www.aplustopper.com\/area-of-trapezium\/","name":"How To Find Area Of Trapezium - 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