Question

ABCD is a parallelogram and AF || DE. Prove that area (|| gm DEFH) = area (|| gm ABCD).

[Hint: Each || gm is equal in area to || gm ADEG]

Answer 1

We know that,

Parallelograms on the same base and between the same parallels are equal in area.

Since, || gm ADEG and || gm DEFH are on same base DE and between same parallels AF and DE.

∴ ar(|| gm ADEG) = ar(|| gm DEFH)   ...(i)

Also, || gm ADEG and || gm ABCD are on same base AD and between same parallels AD and BE.

∴ ar(|| gm ADEG) = ar(|| gm ABCD)   ...(ii)

From (i) and (ii),

Area(|| gm DEFH) = Area(|| gm ABCD)