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Question
In Fig. 3, APB and AQO are semicircles, and AO = OB. If the perimeter of the figure is 40 cm, find the area of the shaded region [Use `pi=22/7`]
Solution
Let the radius of the semi-circle APB be r
⇒ The radius of the semi-circle AQO =`r/2`
Now,
Perimeter of the given figure = Length of arc AQO + Length of arc APB + OB
`=pixxr/2+pixxr+r`
`=r(3/2pi+1)`
`=r(3/2xx22/7+1)`
`= r((33+7)/7)`
`=r(40/7)cm`
⇒r=7 cm
∴ Area of the shaded region = Area of semi-circle AQO + Area of semi-circle APB
`=(pi(r/2)^2)/2+(pir^2)/2`
`=(pi(7/2)^2)/2+(pixx7^2)/2`
`=(49pi)/8+(49pi)/2`
`=49pi(1/8+1/2)`
`=49xx22/7xx5/8`
= 96.25 cm2
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