Question

In the given figure, $ABCD$ is a rectangle in which $AB=40cm$ and $BC=25cm$. If P,Q,R.S be the midpoints of AB, BC, CD and DA respectively, find the area of the shaded region.

Answer 1

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

Here, $AB=DC=SQ=40cm$
$AD=BC=RP=25cm$
Also, $OP=OR=\frac{RP}{2}=\frac{25}{2}=12.5cm$
From the figure we observe:
Area of $\Delta SPQ=$ Area of $\Delta SRQ$
∴ Area of the shaded region $=2\times$(Area of $\Delta SPQ$)
$=2\times (\frac{1}{2}\times SQ\times OP)$
$=2\times (\frac{1}{2}\times 40cm\times 12.5cm)$
$=500c{m}^2$