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Question

Find the area of the shaded region in Fig. 12.21, if ABCD is a square of side 14 cm and APD and BPC are semicircles.

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Solution

There are two semicircles in the figure.
Side of the square = 14 cm
Diameter of the semicircle = 14 cm
Radius of the semicircle = 7 cm
Area of the square =14×14=196 cm2
Area of the semicircle =(πR2)2
=(227×7×7)2cm2=77 cm2
Area of two semicircles
=2×77 cm2=154 cm2
Area of the shaded region
= Area of the square - Area of the semicircles
=196 cm2154 cm2=42 cm2

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