Find the total surface area of a triangular prism whose base is a right‑angled triangle with legs 7 cm and 24 cm, and whose height is 12 cm.

Step-by-step solution

1. Calculate the area of the triangular base: $A_{\text{base}}=\frac{1}{2}\times 7\times 24=84$ cm${}^2$.
2. Determine the hypotenuse: $\sqrt{7^2+24^2}=\sqrt{625}=25$ cm.
3. Find the perimeter of the triangle: $7+24+25=56$ cm.
4. Use the surface area formula for a prism: $S=2A_{\text{base}}+P\times h$.
5. Compute $2A_{\text{base}}=2\times 84=168$ cm${}^2$.
6. Compute the lateral area: $P\times h=56\times 12=672$ cm${}^2$.
7. Add them: $168+672=840$ cm${}^2$.
8. So the total surface area is $840$ square centimetres.

Concept tested: Surface area of triangular prism

Published 10 October 2026 · How this solution was prepared and checked