1. **Stating the problem:** Find the surface area of a triangular prism. 2. **What is a triangular prism?** It is a 3D shape with two triangular bases and three rectangular faces connecting them. 3. **Formula for surface area:** The surface area $SA$ of a triangular prism is the sum of the areas of the two triangular bases plus the areas of the three rectangular faces. $$SA = 2 \times \text{Area of triangle base} + \text{Perimeter of triangle base} \times \text{length of prism}$$ 4. **Area of triangle base:** If the triangle has base $b$ and height $h$, then $$\text{Area of triangle} = \frac{1}{2} b h$$ 5. **Perimeter of triangle base:** Sum of the lengths of the three sides of the triangle, say $a$, $b$, and $c$: $$P = a + b + c$$ 6. **Putting it all together:** $$SA = 2 \times \frac{1}{2} b h + (a + b + c) \times l = b h + (a + b + c) l$$ where $l$ is the length of the prism. 7. **Example:** If the triangular base has sides $a=3$, $b=4$, $c=5$, height $h=2.4$, and prism length $l=10$: Calculate area of triangle base: $$\frac{1}{2} \times 4 \times 2.4 = 4.8$$ Calculate perimeter: $$3 + 4 + 5 = 12$$ Calculate surface area: $$SA = 2 \times 4.8 + 12 \times 10 = 9.6 + 120 = 129.6$$ 8. **Summary:** To find the surface area of a triangular prism, calculate the area of the two triangular bases and add the area of the three rectangular faces formed by the perimeter of the triangle times the prism length.