Q18 of 31 Page 1

Find the area of shaded region shown 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.

Area of shaded region


= Area of equilateral triangle OAB + Area of major sector


Given


Radius of circle, r = 6 cm


Side of equilateral triangle, a = 12 cm


Also,


Sector angle, θ = 360° – ∠OAB


⇒ θ = 360° – 60° = 300° [Angle of equilateral triangle = 60°]


Formulas


Area of equilateral triangle


Where a is side of the circle.


Area of sector of circle


Where θ is the sector angle and r is the radius of circle


⇒ Area of shaded region




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