2 A uniform lamina \(A B C D\) consists of a semicircle \(B C D\) with centre \(O\) and diameter 0.4 m , and an isosceles triangle \(A B D\) with base \(B D = 0.4 \mathrm {~m}\) and perpendicular height \(h \mathrm {~m}\). The centre of mass of the lamina is at \(O\).
- Find the value of \(h\).
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The lamina is suspended from a vertical string attached to a point \(X\) on the side \(A D\) of the triangle (see diagram). Given the lamina is in equilibrium with \(A D\) horizontal, calculate \(X D\).