Find the area of shaded region in figure, where a circle of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm
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In the given figure,
radius (r) = 6cm
Side of equilateral triangle (a) = 12cm
It can be observed that area of shaded region = Area of triangle - Area of Minor segment + Area of major segment
Area of eqilateral ∆ = √3/4 * a²
= √3 * 12 * 3 = 36√3 = 62.46 cm²
Area of minor segment = Theta/360° * πr², here theta = 60° because it ∆ABC is equilateral
= 1/6 * 36 * 3.14 = 18.84 cm²
Area of major sector = 360° - Theta * πr² = 300/360 * 3.14 * 36
= 94.2 cm²
Hence, area of shaded region = 62.46 - 18.84 + 94.2
= 43.62 + 94.2 = 137.82 cm²
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