![\"\"](\"https:\/\/i1.wp.com\/www.worksheetsbuddy.com\/wp-content\/uploads\/2021\/01\/parallelograms-on-same-base-and-between-same-parallels-1.jpg?resize=300%2C280&ssl=1\")
<\/p>\nStudents can check how parallelograms having the same base and between the same parallels are equal in area and proof for that. When two or more parallelogram lies on the same base and between same parallels then they have the same area. Also, find the solved example questions here explaining the concept and learn the concept behind them.<\/p>\n
Let us draw a parallelogram ABCD on a cardboard sheet or thick sheet of paper.<\/p>\n
<\/p>\n
Now, draw a line segment DE as shown in the figure.<\/p>\n
![\"\"](\"https:\/\/i1.wp.com\/www.worksheetsbuddy.com\/wp-content\/uploads\/2021\/01\/parallelograms-on-same-base-and-between-same-parallels-2.jpg?resize=300%2C266&ssl=1\")
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Now, cut the triangle ADE congruent to triangle ADE in a seperate sheet with the help of a tracing paper and place the triangle ADE in such a way that AD coincides BC. The entire process is as shown below.<\/p>\n
![\"\"](\"https:\/\/i1.wp.com\/www.worksheetsbuddy.com\/wp-content\/uploads\/2021\/01\/parallelograms-on-same-base-and-between-same-parallels-3.jpg?resize=300%2C216&ssl=1\")
<\/p>\n
Note that there are two parallelograms ABCD and EE\u2019CD on the same base CD and between the same parallel AE\u2019 and CD.<\/p>\n
\u2206ADE \u2245 \u2206 A\u2019 D\u2019 E\u2019<\/p>\n
Therefore, Area of ADE = Area of A\u2019D\u2019E\u2019<\/p>\n
Also, Area of ABCD = Area of ADE + Area of EBCE<\/p>\n
= Area of A\u2019D\u2019E\u2019 + Area of EBCD<\/p>\n
= Area of EE\u2019CD<\/p>\n
So, the two parallelograms are in an equal area.<\/p>\n
Example 1:<\/strong><\/p>\n A farmer was having a field in the form of a parallelogram ABCD. She took any point P on AB and joined it to points C and D. In how many parts the fields are divided? What are the shapes of these parts? The farmer wants to sow wheat and pulses in equal portions of the field separately. How should she do it?<\/p>\n Solution:<\/strong><\/p>\n If DP and CP are joined parallelogram ABCD is divided into three triangles.<\/p>\n They are \u25b3 APD, \u25b3 CDP, \u25b3 BCP<\/p>\n \u25b3 CDP and parallelogram ABCD are on the same base i.e CD and between parallel sides CD \u2225 AC<\/p>\n \u2234 Area of \u25b3 CDP = 1\/2 x area of parallelogram ABCD \u2014- (i)<\/p>\n \u2234 Area of \u25b3 APD + Area of \u25b3 BCP = 1\/2 x area of parallelogram ABCD \u2014- (ii)<\/p>\n From equation (i) and equation (ii)<\/p>\n Area of \u25b3 CDP = Area of \u25b3 APD + Area of \u25b3 BCP<\/p>\n \u2234 The farmer can use the part of the field to sow wheat, i.e. Area of \u25b3 APD + Area of \u25b3 BCP, and in the same area he can use the Area of \u25b3 CDP to sow pulses.<\/p>\n Example 2:<\/strong><\/p>\n Parallelograms ABCD and ABEF are situated on the opposite sides of AB in such a way that D, A, F are not collinear. Prove that DCEF is a parallelogram, and parallelogram ABCD + parallelogram ABEF = parallelogram DCEF.<\/p>\n Solution:<\/strong><\/p>\n AB and DC are two opposite sides of parallelogram ABCD,<\/p>\n Therefore, AB \u2225 DC and AB = DC<\/p>\n Again, AB and EF are two opposite sides of parallelogram ABEF<\/p>\n Therefore, AB \u2225 EF and AB \u2225 EF<\/p>\n Therefore, DC \u2225 EF and DC = EF<\/p>\n Therefore, DCEF is a parallelogram.<\/p>\n Therefore, \u2206ADF and \u2206BCE, we get<\/p>\n AD = BC (opposite sides of parallelogram ABCD)<\/p>\n AF = BE (opposite sides of parallelogram ABEF)<\/p>\n And DF = CE (opposite sides of parallelogram CDEF)<\/p>\n Therefore, \u2206ADF \u2245 \u2206BCE (side \u2013 side \u2013 side)<\/p>\n Therefore, \u2206ADF = \u2206BCE<\/p>\n Therefore, polygon AFECD \u2013 \u2206BCE = polygon AFCED \u2013 \u2206ADF<\/p>\n Parallelogram ABCD + Parallelogram ABEF = Parallelogram DCEF<\/p>\n","protected":false},"excerpt":{"rendered":" Students can check how parallelograms having the same base and between the same parallels are equal in area and proof for that. When two or more parallelogram lies on the same base and between same parallels then they have the same area. Also, find the solved example questions here explaining the concept and learn the … Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/35628"}],"collection":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/comments?post=35628"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/35628\/revisions"}],"predecessor-version":[{"id":138445,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/35628\/revisions\/138445"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=35628"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=35628"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=35628"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"https:\/\/i1.wp.com\/www.worksheetsbuddy.com\/wp-content\/uploads\/2021\/01\/parallelograms-on-same-base-and-between-same-parallels-4.jpg?resize=300%2C240&ssl=1\")
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