Question

Find the area of the
shaded region.
(1 = 3.14, 13 = 1.73)
- 12 cm
[Oct 12]
360°​

Answer 1

Answer:

OAB is an equilateral triangle with each angle equal to 60°.

Area of the sector is common in both.

Radius of the circle = 6 cm.

Side of the triangle = 12 cm.

Area of the equilateral triangle = √3/4 × (OA)2 = √3/4 × 122 = 36√3 cm2

Area of the circle = π R2 = 22/7 × 62 = 792/7 cm2

Area of the sector making angle 60° = (60°/360°) × π r2 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

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