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A uniform lamina \(A B C D E\) consists of a rectangle \(A B D E\) and an isosceles triangle \(B C D\) joined along their common edge. \(A B = D E = 8 \mathrm {~cm} , A E = B D = 10 \mathrm {~cm}\) and \(B C = C D = 13 \mathrm {~cm}\) (see diagram).
- Find the distance of the centre of mass of the lamina from \(A E\).
- The lamina is freely suspended from \(B\) and hangs in equilibrium. Calculate the angle that \(B D\) makes with the vertical.