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=196cm2
Area of the semicircle =(πR2)2 =(227×7×7)2cm2=77cm2
Area of two semicircles =2×77cm2=154cm2
Area of the shaded region
= Area of the square - Area of the semicircles =196cm2−154cm2=42cm2