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Explanation:

Let ‘a’ be the side of the triangle.

Circum-radius of an equilateral triangle = a/√3
∴ Area of the circum-circle = π × (a/√3)2 = πa2/3

In-radius of an equilateral triangle = a/2√3
∴ Area of the in-circle = π × (a/2√3)2 = πa2/12

According to the question,

πa2/3 - πa2/12 = 2156

⇒ πa2/4 = 2156

⇒ a2 = 2156 × 4 × 7/22 = 2744

∴ Area of the equilateral triangle = √3/4 × a2 = √3/4 × 2744 = 686√3.

Hence, option (a).

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