Calculate the total surface area of a triangular prism whose base is a right‑angled triangle with legs 5 cm and 12 cm, and whose height is 9 cm.

Step-by-step solution

1. Determine the area of one right‑angled triangle base: $\frac{1}{2}\times 5\times 12=30$ cm\textsuperscript{2}.
2. Since there are two identical triangular faces, total area of these faces: $2\times 30=60$ cm\textsuperscript{2}.
3. Find the perimeter of the triangular base: $5+12+\sqrt{5^2+12^2}=5+12+13=30$ cm.
4. Compute the lateral area by multiplying perimeter with prism height: $30\times 9=270$ cm\textsuperscript{2}.
5. Add the areas of the triangular faces and the lateral area: $60+270=330$ cm\textsuperscript{2}.
6. Answer: $330$ cm\textsuperscript{2}.

Concept tested: Surface area of triangular prism

Published 16 October 2026 · How this solution was prepared and checked