Nets and exposed surface area

A net unfolds a solid into its faces. For a closed right prism, the two end faces contribute \(2A\); the rectangular side faces have common length \(L\) and combined width equal to the cross-section perimeter \(P\). Thus total surface area is \(2A+PL\).

Example

The 3–4–5 triangular prism of length 10 cm has surface area \(2(6)+(3+4+5)10=132\text{ cm}^2\). Each triangular end is 6 cm²; its three side faces are 30, 40 and 50 cm².

An open container has no lid to count. A cuboid box 5 cm by 3 cm by 2 cm, open on top, has exposed outer area \(5(3)+2(5)(2)+2(3)(2)=47\text{ cm}^2\), ignoring wall thickness. The formula for a closed cuboid would incorrectly add another 15 cm².