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In the given figure, are shown two arcs ...

In the given figure, are shown two arcs PAQ and PBQ. Arc PAQ is a part of circle with centre O and radius OP while are PBQ is a semi-circle drawn on PQ as diameter with centre M. OP=PQ=10 cm show that area of shaded region is `25(sqrt3-pi/6) cm^2`

Text Solution

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From the diagram, we can see that,
Area of the shaded region`(A) =` Area of triangle `OPQ` +Area of semi circle `PBQ` - Area of sector `OPQ`
`=>A = sqrt3/4(10)^2 + (pi(5)^2)/2 - 60/360 *pi(10)^2`
`=>A = 25sqrt3 + 25/2pi - 50/3pi`
`=>A = 25sqrt3 - 25/6pi`
`=A = 25(sqrt3 - pi/6)`
So, area of the shaded region is `25(sqrt3 - pi/6) cm^2`.
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