Question

In the given figure, ABCD and AEFD are two parallelograms. Prove that ar (∆PEA) = ar (∆QFD).

Answer 1

Given: ABCD and AEFD are two parallelograms.

To prove: ar (∆PEA) = ar (∆QFD)

Proof: In quadrilateral PQDA,

AP || DQ (∵ in parallelogram ABCD, AB || CD)

and PQ || AD (∵ in parallelogram AEFD, FE || AD)

So, PQDA is a parallelogram.

Also, parallelogram PQDA and AEFD are on the same base AD and between same parallels AD and EQ.

ar (||gm PQDA) = ar (||gm AEFD)

On subtracting ar (quadrilateral APFD) from both sides, we get

ar (||gm PQDA) – ar (quadrilateral APFD) = ar (||gm AEFD) – ar (quadrilateral APFD)

⇒ ar (∆QFD) = ar (∆PEA)

Hence proved.