Question

Find the area of the shaded region in the 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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Answer 1

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Find the area of the shaded region in the 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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Here we can see that

Area of required figure = Area of circle+Area of triangle− Area of the sector

⇒A(circle)=πr²

⇒A(circle)=π6²

⇒A(circle)=36π

⇒A(triangle)= (√3/4)a²

⇒A(triangle)= (√3/4)×12²

⇒A(triangle)=36√3

⇒A(sector)= (1/2)r²θ

⇒A(sector)= 1/2(6²) π/3

⇒A(sector)=6π

Therefore, Required Area=36π+36√3. -6π

⇒ Required Area=30π+36√3

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Answer 2

Find the area of the shaded region in the 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?

Ans : Here we can see that,

Area of required figure = Area of circle+Area of triangle− Area of the sector

⇒A(circle)=πr²

⇒A(circle)=π6²

⇒A(circle)=36π

⇒A(triangle)= (√3/4)a²

⇒A(triangle)= (√3/4)×12²

⇒A(triangle)=36√3

⇒A(sector)= (1/2)r²θ

⇒A(sector)= 1/2(6²) π/3

⇒A(sector)=6π

Therefore, Required Area=36π+36√3. -6π

⇒ Required Area=30π+36√3