Question

ABCD is a given rectangle with length as 80 cm and breadth as 60 cm. P, Q, R, S are the mid-points of sides AB, BC, CD, DA, respectively.

A circular rangoli of radius 10 cm is drawn at the centre as shown in the given figure. Find the area of shaded portion.

Answer 1

Here, AP $=\frac{1}{2}$ AB $=\frac{1}{2}\times 80=40cm$

Also, AS $=\frac{1}{2}$ AD $=\frac{1}{2}\times 60=30cm$

Area of $\Delta APS=\frac{1}{2}\times AP\times AS=\frac{1}{2}\times 40\times 30=600c{m}^2$

Area of portion PQRS = Area of rectangle ABCD - 4 $\times$ Area of $\Delta APS=80\times 60-4\times 600$

$=4800-2400=2400c{m}^2$

Area of circular rangoli $=\pi \times (10{)}^2=\frac{22}{7}\times 100=314c{m}^2$ [$\therefore$ radius of circle = 10 cm]

$\therefore$ Area of shaded region = 2400 - 314 = 2086 $c{m}^2$