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Question
Find the area of the shaded region in the given figure, where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre [Use Π = 22/7]
Solution
We know that each interior angle of an equilateral triangle is of measure 60°.
Area of sector OCDE = `60^@/360^@pir^2`
`=1/6xx22/7xx6xx6`
`= 132/7 cm^2`
Area of triangleOAB = `sqrt3/4(12)^2 = (sqrt3xx12xx12)/4 = 36sqrt3 cm^2`
Area of circle = `pir^2 = 22/7xx6xx6 = 792/7 cm^2`
Area of shaded region = Area of ΔOAB + Area of circle − Area of sector OCDE
`= 36sqrt3 + 792/7 - 132/7`
`=(36sqrt3 + 660/7) cm^2`
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