In the given figure, ABCD, ABEF and AGHF are parallelograms.

Prove that the area of parallelogram ABCD = area of parallelogram AGHF.

Given: ABCD, ABEF and AGHF are parallelograms.

To prove: Area of parallelogram ABCD = area of parallelogram AGHF.

Proof: In parallelograms ABCD and ABEF, AB is the same base and they lie between the same parallel lines AB and DE.

∴ Area of ABCD = Area of ABEF ……………….(1)

Similarly, in parallelograms ABEF and AGHF, AF is the same base and they lie between same parallel line AF and BH.

∴ Area of ABEF = Area of AGHF ……………….(2)

From equations (1) and (2), we get:

Area of ABCD = Area of ABEF = Area of AGHF

Hence, area of parallelogram ABCD = area of parallelogram AGHF.