The diagram shows a symmetrical metal plate. The plate is made by removing two identical pieces from a circular disc with centre C. The boundary of the plate consists of two arcs PS and QR of the original circle and two semicircles with PQ and RS as diameters. The radius of the circle with centre C is 4 cm, and PQ = RS = 4 cm also.

(a) Show that angle PCS = \(\frac{2}{3} \pi\) radians.

(b) Find the exact perimeter of the plate.

(c) Show that the area of the plate is \(\left( \frac{20}{3} \pi + 8\sqrt{3} \right) \text{ cm}^2\).