Question

4. Find the area of the shaded region in Fig. 12.22, 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.​

Answer 1

Given:  a circular arc of radius 6 cm has  been drawn with vertex O of an equilateral triangle OAB of side 12 cm

To Find : area of the shaded region

Solution:

area of the shaded region =

Area of Circle + area of Triangle - Area of Sector ODE

Area of Circle = π(6)²  = 36π = 113.04 cm²

Area of Sector = (60/360) π(6)² = 6π = 18.84 cm²

Area of Triangle = (√3 / 4)12² = 36√3 = 62.35 cm²

area of the shaded region =   113.04 + 62.35 -  18.84

=> area of the shaded region = 156.55 cm²

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Answer 2

❥QUESTION

Find the area of the shaded region in Fig. 12.22, 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.​

❥Answer

It is given that OAB is an equilateral triangle having each angle as 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= (√3/40×122 = 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