The lamina \(B F D E\) is obtained by removing triangles \(A E D\) and \(B C F\) from a uniform square lamina \(A B C D\) of side \(2 a\). The length of side \(A E\) is \(a\) and the length of side \(F C\) is \(h\) (see diagram). The centre of mass of \(B F D E\) is at a distance \(\bar{x}\) from \(A D\), and at a distance \(\bar{y}\) from \(A B\). (a) Show that \(\bar{x}=\frac{h^{2}-6 a h+11 a^{2}}{3(3 a-h)}\) and find a corresponding expression for \(\bar{y}\).

(b) The lamina \(B F D E\) is placed vertically on its edge \(E B\) on a smooth horizontal surface.

Find, in terms of \(a\), the set of possible values of \(h\) for which the lamina remains in equilibrium.