A uniform lamina \(A E C F\) is formed by removing two identical triangles \(B C E\) and \(C D F\) from a square lamina \(A B C D\). The square has side \(3 a\) and \(E B=D F=h\) (see diagram).
(a) Find the distance of the centre of mass of the lamina \(A E C F\) from \(A D\) and from \(A B\), giving your answers in terms of \(a\) and \(h\).

The lamina \(A E C F\) is placed vertically on its edge \(A E\) on a horizontal plane.
(b) Find, in terms of \(a\), the set of values of \(h\) for which the lamina remains in equilibrium.