Question

ABCD is a rectangle having length 30 cm and breadth 25 cm. P, Q, R and S are the midpoints of AB, BC, CD, and AD, respectively. What is the area of the shaded portion?
(4 marks)

Answer 1

Given:
Length of the rectangle ABCD = AB = SQ = DC = 30 cm
Breadth of the rectangle ABCD = AD = PR = BC = 25 cm
(0.5 marks)

PQRS can be considered as the combination of two triangles i.e., $△PSR$ and $△PQR$
Here, PR is the base of the two triangles.

Area of $\Delta PQR=\frac{1}{2}\times PR\times height$

$=\frac{1}{2}\times 25\times 15$

$=\frac{375}{2}c{m}^2$
(1 mark)

Similarly, area of $\Delta PSR=\frac{1}{2}\times PR\times height$

$=\frac{1}{2}\times 25\times 15$

$=\frac{375}{2}c{m}^2$

(1 mark)

$\therefore$ The area of shaded portion = Area of rectangle - (area of $\Delta PQR$ + area of $\Delta PSR$)

$=(30\times 25)-(\frac{375}{2}+\frac{375}{2})$

$=(750-375)c{m}^2=375c{m}^2$
(1.5 marks)