(i)[2]
Calculate the distance from $AD$ to the centre of mass of the prism.
(ii)[2]
Express the distance from $AB$ to the centre of mass of the prism in terms of $a$.
(iii)[3]
The prism weighs $18\,\text{N}$ and is in equilibrium on a rough horizontal surface, with $AD$ touching the surface. A horizontal force of magnitude $6\,\text{N}$ is applied to the prism. This force passes through the centre of mass in the direction $BC$. Given that the prism is on the point of toppling, calculate $a$.