In an equilateral triangle three coins are of radii 1 unit each are kept so that they touch the sides of the triangle as well as each other

Question

Find the area of the triangle:

Answer 1

The line joining the vertex of the triangle and the centre of the coin makes angle π/6 with the sides of the triangle.

The length of each side of the equilateral triangle is 2 + 2 cot π/6 = 2(1 + √3).

Hence its area is √3/4 * (side length)² = √3/4*4(1+√3)² = 6+ 4√3

Comments

How u take the sides of the equilateral triangle as  2+2cot pi/6?

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check the figure carefully and considering angle for the side you will get the length as given in answer