2025 WGS P1 Q13

The diagram shows a windowpane which is formed by a rectangle with sides \(2x\) m by \(y\) m, and a semicircle of radius \(x\) m.

The perimeter of the window is 12 m.

1. Show that \(y=\dfrac12(12-2x-\pi x)\).[2]
2. Hence show that the area, \(A\text{ m}^2\), of the windowpane is \(A=12x-2x^2-\dfrac{\pi x^2}2\).[2]
3. Find the value of \(x\) for which \(A\) has a stationary value, correct to 2 significant figures.[3]
4. Determine whether the stationary value of \(A\) is a maximum or a minimum.[2]