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Question
In the given figure, ABCD is 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.
Solution
Area of the shaded region = Area of the rectangle − Area of the semicircle
`= 21 xx 14 - {1/2xx pi xx(14/2)^2}`
`=294 - {1/2 xx 22/7 xx 7 xx 7}`
= 297- 77
`= 217 cm^2`
Therefore area of shaded region is `217 cm^2`
= AB + AD + DC + BC
`= AB + AD + DC + 1/2 xx 2pi (14/2)`
`= 21 + 14 + 21 + 22/7 xx 7`
= 56 + 22
= 78 cm
Therefore the perimeter of the shaded region is 78 cm
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