Question

In Fig. 32, ABCD is a rectangle of length AB = 40 cm and breadth BC = 25 cm. If P, Q, R, S be the mid-points of the sides AB, BC, CD and DA respectively, find the area of the shaded region.

Answer 1

We have,
Join points PR and SQ.
These two lines bisect each other at point O.

Here, AB = DC = SQ = 40 cm and AD = BC =RP = 25 cm
Also OP = OR = $\frac{RP}{2}=\frac{25}{2}=12.5\mathrm{cm}$
From the figure we observed that,
Area of Δ SPQ = Area of Δ SRQ
Hence, area of the shaded region = 2 x (Area of Δ SPQ)
= 2 x ($\frac{1}{2}$ x SQ x OP)
= 2 x ($\frac{1}{2}$ x 40 cm x 12.5 cm)
= 500 cm²