Volume and Surface Area of Composite Solids

The two figures below show two solids that are the remaining parts of two identical cuboids, where two identical triangular prisms with right-angled triangular base is carved out in different ways.

Given that the dimensions of the base triangle of the triangular prisms are \(12\) cm by \(16\) cm by \(20\) cm, and the height of the cuboids and triangular prisms are \(x\) cm, show that the difference between the total surface area of the two solids is \(40x\) cm\(^2\).

Correction: the source claim omits the factor \(x\). The difference is \(40x\text{ cm}^2\), as the solution shows.