Question

find the area of the shaded area 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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Answer 1

Answer:

1. 660/7 + 36√3

Step-by-step explanation:

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closed Find the area of the shaded region , 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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asked Mar 8, 2016 in Class X Maths by bhai Basic (90 points)

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answered Mar 9, 2016 by Pranav lunawat Mature (287 points)

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