1
\(A B C D\) is a uniform lamina with \(A B = 1.8 \mathrm {~m} , A D = D C = 0.9 \mathrm {~m}\), and \(A D\) perpendicular to \(A B\) and \(D C\) (see diagram).

1. Find the distance of the centre of mass of the lamina from \(A B\) and the distance from \(A D\). The lamina is freely suspended at \(A\) and hangs in equilibrium.
2. Calculate the angle between \(A B\) and the vertical.