In the given figure, AB ∥ DC ∥ EF, AD ∥ BE and DE ∥ AF. Prove that : ar (∥ gm DEFH) = ar (∥ gm ABCD).

We know that,

AD || BE ⇒ AD || EG

ED || FA ⇒ ED || GA

Since, opposite sides are parallel.

Hence, ADEG is a parallelogram.

Since ||gm ABCD and ||gm ADEG lie on same base AD and between same parallel lines AD and EB,

area of ||gm ABCD = area of ||gm ADEG …….(1)

We know that,

ED || FA ⇒ DE || FH

DC || EF ⇒ DH || EF

Since, opposite sides are parallel.

Hence, DEFH is a parallelogram.

Since ||gm DEFH and ||gm ADEG lie on same base DE and between same parallel lines DE and FA,

area of ||gm DEFH = area of ||gm ADEG ……..(2)

From (1) and (2) we get,

⇒ area of ||gm ABCD = area of ||gm DEFH

Hence, proved that area of ||gm ABCD = area of ||gm DEFH.