Derive an expression for the failure moment per unit area

Question

Consider a box-beam with constant area A, and variable depth h, width b, and thickness t.

(a) Derive an expression for the moment of inertia per unit area in terms of the ratio r = h/b.

(b) Derive an expression for the failure moment per unit area in terms of the ratio r = h/b, for a constant material strength Fx.

(c) Comment on the significance of your results with regard to thin-walled construction.