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Question
In the given figure, APB and CQD are semicircles of diameter 7 cm each, while ARC an BSD are semicircles of diameter 14 cm each. Find the
- perimeter
- area of the shaded region.
Solution
i . Perimeter of shaded region = Length of the arc APB + Length of the arc ARC + Length of the arc BSD + Length of the arc CQD
`=1/2xx2pi"r"_1 + 1/2xx2pi"r"_2 + 1/2xx2pi"r"_4`
`=1/2xx2pi(7/2) + 1/2xx2pi(7)+1/2xx2pi(7/2)`
`=2pi(7/2)+2pi(7)`
`=2pi(7/2+7)`
`=2xx22/7xx21/2`
= 66 cm
ii . Area of shaded region = Area of the arc ARC + Area of the arc BSD - (Area of the arc APB + Area of the arc CQD)
`=1/2xxpi("r"_1)^2+1/2xxpi("r")^2 - [1/2xxpi("r"_3)^2 + 1/2xxpi("r"_4)^2]`
`=1/2xxpi(7)^2+1/2xxpi(7)^2 - [1/2xxpi(7/2)^2+1/2xxpi(7/2)^2]`
`= pi(7)^2 - pi(7/2)^2`
`=pi(49 - 49/4)`
`=22/7xx147/4`
= 115.5 cm2
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