In the given figure, the side of square is 28 cm and radius of each circle is half of the length of the side of the square where O and O′ are centers of the circles. Find the area of shaded region.
Given: Side of the square = 28 cm
∴ Area of the square = (Side)2 = (28 cm)2 = 784 cm2
Radius of each circle = 1/2 (Side of the square) = 1/2 × (28) = 14 cm
∴ Area of one circle = πr2 = (22/7) × 14 × 14 = 616 cm2
Thus, area of two circles = 616 × 2 = 1232 cm2
Angle subtended by the sector of the circle at the center = θ
= 90° = π/2 radian
Area of one sector = (1/2) × r2 × θ
= (1/2) × 14 × 14 × (π/2)
= (1/2) × 14 × 14 × (1/2) × (22/7)
= 154 cm2
Area of the shaded region = Area of two circles + Area of the square – 2(Area of the sector of the circle)
= {1232 + 784 – 2(154)} cm2
= 1708 cm2