N2015 P1 Q4

A piece of wire of fixed length \(d\text{ m}\) is cut into two parts. One part is bent into the shape of a rectangle with sides of length \(x\text{ m}\) and \(y\text{ m}\). The other part is bent into the shape of a semicircle, including its diameter. The radius of the semicircle is \(x\text{ m}\). Show that the maximum value of the total area of the two shapes can be expressed as \(kd^2\text{ m}^2\), where \(k\) is a constant to be found.[6]