Q45 of 45 Page 12

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.

(CBSE 2017)

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

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