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25/06/2021 1:49 pm
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Find the area of the shaded region in 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.
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25/06/2021 1:51 pm
It is given that OAB is an equilateral triangle having each angle as 60°
Radius of the circle = 6 cm.
Side of the triangle = 12 cm.
Area of the equilateral triangle = (√3/4) (OA)2
= (√3/40 × 122) = 36√3 cm2
Area of the circle = πR2 = (22/7) × 62
= 792/7 cm2
Area of the sector making angle 60° = (60°/360°) ×πr2 cm2
= (1/6)×(22/7) × 62 cm2
= 132/7 cm2
Area of the shaded region = Area of the equilateral triangle + Area of the circle – Area of the sector
= 36√3 cm2 + 792/7 cm2 - 132/7 cm2
= (36√3 + 660/7) cm2