`A B C D` is a parallelogram, `G` is the point on `A B` such that `A G=2 GB , E ` is a point of `D C` such that `C E=2D E` and` F` is the point of `B C` such that `B F=2F Cdot` Prove that: `ar (A D E G)= ar (GBCE)`

Explanation

Solution: ABCD is a parallelogram in which AB||CD and AB=CD

`therefore BG=1/3CD=1/3AB`

BG = DE

ADEH is a parallelogram

(Since, AH is parallel to DE and AD is parallel to HE)

Area of parallelogram ADEH = Area of parallelogram BCIG ____1

(Since, DE = BG and AD = BC parallelogram with corresponding sides equal)

Area (`triangleHEG`) = Area (`triangleEGI`) ______2

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