Q30 of 45 Page 12

In Fig. 4, ABCD is a square of side 14 cm. Semi-circles are drawn with each side of the square as diameter. Find the area of the shaded region.

(CBSE 2016)

On the basis of given conditions in the question the figure can be drawn as follows:


It is given in the question that,


Radius of circle,



As the radius of all the semi-circles is same


∴ Area of 4 semi-circles = AOB + DOC + AOD + BOC


We know that, Area of semi-circle =


∴ Area of 4 semi–circles =



= 4 × 77


= 308 cm2


Also we know that, area of Square = (Side)2


∴ Area of square, ABCD = 14 × 14


= 196 cm2


Hence, Area of shaded region = 2 (Area of square) – 4 (Area of semi-circle)


= 2 × 196 – 308


= 392 – 308


= 84 cm2

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(CBSE 2018)