**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