ABC is an equilateral triangle with side 2 cm. With A, B and C as centres and radius 1 cm three arcs are drawn. The area of the region with in the triangle bounded by three arcs isa)b)c)d)Correct answer is option 'C'. Can you explain this answer?

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ABC is an equilateral triangle with side 2 cm. With A, B and C as centres and radius 1 cm three arcs are drawn. The area of the region with in the triangle bounded by three arcs is

Correct answer is option 'C'. Can you explain this answer?

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ABC is an equilateral triangle with side 2 cm. With A, B and C as cent...

ABC is an equilateral triangle
Given,
AB = BC = CA = 2 cm
∠A = ∠B = ∠C = 60°
Height of equilateral triangle = (√3/2) × (side)
= (√3/2) × 2 = √3 cm
∴ Area of the triangle = (1/2) × √3 × 2 = √3 cm²
Area inside the triangle inscribed by three arcs = 3 × area of one arc
= 3 × (θ/360°) × πr²
= 3 × π × 1² × (60/360) = π/2
∴ Required area = (√3 - π/2) cm²

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ABC is an equilateral triangle with side 2 cm. With A, B and C as centres and radius 1 cm three arcs are drawn. The area of the region with in the triangle bounded by three arcs isa)b)c)d)Correct answer is option 'C'. Can you explain this answer?

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