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.

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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 =

Area of square ABCD = (Side)² = (14)² = 196 cm²

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 cm²

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