Question

In the given figure, four equal circles are described about the four corners of a square so that each circle touches two of the circle as shown in the figure. find the area of the shaded region, each side of the square measuring 14 cm.

Answer 1

Area of each of the four quadrants is equal to each other with radius 7 cm.

Area of the square ABCD = (Side)² = (14 cm)² = 196 cm²
Sum of the areas of the four quadrants = $\left(4\times \frac{1}{4}\times \frac{22}{7}\times 7\times 7\right)$ cm²
= 154 cm²
∴ Area of the shaded portion = Area of square ABCD - Areas of the four quadrants
= (196 - 154) cm²
= 42 cm²