Find the area of the shaded region in the given figure, if ABCD is a square of side 14 cm and APD and BPC are semicircles. [Use Π = 22/7]

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#### Solution

It can be observed from the figure that the radius of each semi-circle is 7 cm.

Area of each semi-circle = `1/2 pir^2`

`= 1/2xx22/7xx(7)^2`

= 77 cm^{2}

Area of square ABCD = (Side)^{2} = (14)^{2} = 196 cm^{2}

Area of the shaded region

= Area of square ABCD − Area of semi-circle APD − Area of semi-circle BPC

= 196 − 77 − 77 = 196 − 154 = 42 cm^{2}

Concept: Areas of Combinations of Plane Figures

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