(a) Each arc is part of a circle with a central angle of 60 degrees (since ABC is equilateral). The length of one arc is \(\frac{60}{360} \times 2\pi \times 2 = \frac{2\pi}{3}\). The perimeter of the coin is the sum of the lengths of the three arcs: \(3 \times \frac{2\pi}{3} = 2\pi\).

(b) The area of one sector is \(\frac{1}{2} \times 2^2 \times \frac{\pi}{3} = \frac{2\pi}{3}\). The area of the equilateral triangle is \(\frac{1}{2} \times 2 \times 2 \times \sin\left(\frac{\pi}{3}\right) = \sqrt{3}\). The area of the coin is the area of three sectors minus the area of the triangle: \(3 \times \frac{2\pi}{3} - \sqrt{3} = 2\pi - 2\sqrt{3}\).