Differentiation - Problems Involving Maximisation and Minimisation

A piece of wire of length \(8\) cm is cut into \(2\) pieces, one of length \(x\) cm, the other \((8 - x)\) cm.
The piece of length \(x\) cm is bent to form a circle with circumference \(x\) cm.
The other piece is bent to form a square with perimeter \((8 - x)\) cm.

Show that, as \(x\) varies, the sum of the areas enclosed by these \(2\) pieces of wire is a minimum when the radius of the circle is \(\frac{4}{4 + \pi}\) cm.