1. **State the problem:** Find the surface area of a triangular prism with triangle side lengths 5 ft, 12 ft, and 13 ft, and prism length 6 ft. 2. **Formula for surface area of a triangular prism:** $$\text{Surface Area} = 2 \times \text{Area of triangular base} + \text{Perimeter of base} \times \text{Length}$$ 3. **Calculate the area of the triangular base:** Since the triangle sides are 5 ft, 12 ft, and 13 ft, it is a right triangle (because $5^2 + 12^2 = 25 + 144 = 169 = 13^2$). Area of right triangle = $\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 5 \times 12 = 30$ ft². 4. **Calculate the perimeter of the triangular base:** $$5 + 12 + 13 = 30 \text{ ft}$$ 5. **Calculate the lateral surface area:** $$\text{Perimeter} \times \text{Length} = 30 \times 6 = 180 \text{ ft}^2$$ 6. **Calculate total surface area:** $$2 \times 30 + 180 = 60 + 180 = 240 \text{ ft}^2$$ **Final answer:** The surface area of the triangular prism is **240 ft²**.