Question

In PQRS, PQ RS, PQ = RS. Diagonals PR and QS intersects at point M. Prove that : A( RMS) = 4 A( PMQ).​

Answer 1

Hint : We will first use congruency to prove coth the triangles equal and we know that congruent figures have equal area and hence proved.

First try to do it yourself and only then move to the given solution.

Solution:

In ∆PMQ and ∆RMS,

PQ = RS (given)

Diagonals of a parallelogram bisect each other.

PM = RM

MQ = MS

By S.S.S , ∆PMQ is congruent to ∆RMS.

We know that congruent figures have equal area.

Hence, Area (∆RMS) = Area (∆PMQ). Proved