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Question
In the given figure, APB and AQO are semicircles and AO = OB. If the perimeter of the figure is 40 cm, find the area of the shaded region.
Solution
Permieter of shaded region = Length of the arc AQO + Length of the arc APB + Length of OB
`=>40=1/2xx2pi("AO"/2) + 1/2xx2pi("OB") +"OB"`
`= 40 = 11/7"AO"+22/7"OB"+"OB"`
`=40 = 11/7"OB "+ 22/7 "OB" + "OB"` [∴ AO = OB]
`=> 40 = 40/7 "OB"`
⇒ OB =7 cm
Area of the shaded portion = Area of semicircle AQO + Area of semicircle APB
`=1/2 pi(7/2)^2 + 1/2(7)^2`
`= 1/2 xx 22/7xx(7/2)^2+1/2xx22/7xx(7)^2`
= 96.25 cm2
Hence, the area of the shaded portion is 96.25 cm2.
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