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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 of an equilateral triangle of side 12 cm as centre and a sector of circle of radius 6 cm with centre B is made.
Solution
In equilateral traingle all the angles are of 60°
∴ ∠ABO = ∠AOB = 60°
Area of the shaded region = (Area of tringle AOB - Area of sector having central angle 60°) +Area of sector having central angle (360° - 60°)
`= sqrt(3)/4("AB")^2 - 60^circ/360^circ pi (6)^2+(300°)/(360°)pi(6)^2`
`=1.73/4(12)^2-1/6xx3.14xx(6)^2+5/6xx3.14(6)^2`
=62.28-18.84 + 94.2
= 137.64 cm2
Hence, the area of shaded region is 137.64 cm2
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