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Question

In the given figure, ABCD is a rectangle of dimensions 21 cm × 14 cm. A semicircle is drawn with BC as diameter. Find the area and the perimeter of the shaded region in the figure. [CBSE 2017]

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Solution

Area of the shaded region

= Area of the rectangle − Area of the semicircle

=21×14-12×π×1422=294-12×227×7×7=294-77=217 cm2

Therefore, area of shaded region is 217 cm2.

Length of the boundary (or perimeter) of the shaded region

=AB+AD+DC+arc BC=AB+AD+DC+12×2π142=21+14+21+227×7=56+22=78 cm

Therefore, the perimeter of the shaded region is 78 cm.


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