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In Figure, A B C D is a quadrilateral ...

In Figure, `A B C D` is a quadrilateral and `B E||A C` and also `B E` meets `D C` produced at `Edot` Show that area of ` A D E` is equal to the area of the quadrilateral `A B C D`

Text Solution

Verified by Experts

We have
`ar(triangleABC)=ar(triangleAEC)`
`[therefore triangle " on the same base and between the same parallels are equal in area"].`
And so, `ar(triangleABC)+ar(triangleADC)=ar(triangleAEC)+ar(triangleADC)`
[adding same areas on both sides]
`rArr ar ("quad.ABCD")=ar(triangleADE)`.
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