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In the trapezium A B C D ,A B C Da n dA...

In the trapezium `A B C D ,A B C Da n dA B=2C Ddot` If the area of ` A O B=84 c m^2,` find the area of ` C O Ddot`

Text Solution

Verified by Experts

In `triangleAOB and triangleCOD`,
`angle1=angle2` (alternate angles)
`angle3= angle4` (alternate angles)
`triangleAOB ~triangleCOD` ( AA corollary)
`(ar(triangleAOB))/(ar(triangleCOD))= (AB^(2))/(CD^(2))`
(ratio of area of two similar triangles is equal to the ratio of square of that corresponding sides)
`((2CD)^(2))/(CD^(2))` ( AB = 2CD, given )
`4/1`
`84/(ar(triangleCOD))=4/1 Rightarrowar(triangleCOD)= 84/4cm^(2)=21cm^(2)`
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