Question

In figure, $A,B,C,D$ are centre of equal circles which touch externally in pairs and $ABCD$ is a square of side $7cm$. Find the area of the shaded region.

Answer 1

Area of square ABCD $=7^2$

$=49c{m}^2$

Radius $=\frac{Sideofsquare}{2}$

$=\frac{7}{2}cm$

Area of 4 quadrant $=4\times \frac{1}{4}\pi r^2$

$=4\times \frac{1}{4}\times \frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}$

$=\frac{77}{2}c{m}^2$

Area o shaded region $=49-\frac{77}{2}$

$=\frac{98-77}{2}$

$=\frac{21}{2}c{m}^2$