Question

In Fig. 12.25, ABCD is a square of side 14 cm. With centers A, B, C and D, four circles are drawn such that each circle touches externally two of the remaining three circles. Find the area of the shaded region.

Answer 1

Side of square = 14 cm
Four quadrants are included in the four sides of the square.
$\therefore$ Radius of the circles $=\frac{14}{2}cm=7cm$
Area of the square $ABCD={14}^2=196c{m}^2$
Area of the quadrant $=(\frac{\pi R^2)}{4}c{m}^2=\frac{(\frac{22}{7}\times 7^2)}{4}c{m}^2$
= $\frac{77}{2}c{m}^2$
Total area of the quadrant $=4\times \frac{77}{2}c{m}^2=154c{m}^2$
Area of the shaded region = Area of the square ABCD - Area of the quadrant
$=196c{m}^2-154c{m}^2=42c{m}^2$