Question

Four equal circles are described about four corners of a square so that each touches two of the others as shown in the fig. Find the area of the shaded portion, each side of the square measuring 28 cm.

Answer 1

Let ABCD be the given square of side a.
$\therefore$ a = 28 cm
$\therefore$ Radius of each circle, r $=\frac{28}{2}$
$=14cm$

Area of the shaded portion = Area of a square - 4 $\times$ Area of a quadrant
$=a^2-4\times \frac{1}{4}\times \pi r^2$
$=28\times 28-4\times \frac{1}{4}\times \frac{22}{7}\times 14\times 14$
$=784-615.44$

$\therefore$ Area of the shaded portion = 168.56 cm${}^2$.