1.

In Figure, `A B C D`is aquadrilateral and `B E|A C`and also `B E`meets `D C`produced at`Edot`Show thatarea of ` A D E`is equal tothe area of the quadrilateral `A B C D`

Answer» 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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