1. **State the problem:** Calculate the surface area of a triangular prism with given side lengths. 2. **Identify the dimensions:** The triangular prism has a triangular base with sides 15 ft, 16 ft, and 17 ft, and the prism length (height) is 20 ft. 3. **Formula for surface area of a triangular prism:** $$\text{Surface Area} = \text{Perimeter of base} \times \text{length} + 2 \times \text{Area of triangular base}$$ 4. **Calculate the perimeter of the triangular base:** $$P = 15 + 16 + 17 = 48 \text{ ft}$$ 5. **Calculate the area of the triangular base using Heron's formula:** - Semi-perimeter: $$s = \frac{P}{2} = \frac{48}{2} = 24$$ - Area: $$A = \sqrt{s(s - 15)(s - 16)(s - 17)} = \sqrt{24 \times 9 \times 8 \times 7}$$ 6. **Simplify the area calculation:** $$A = \sqrt{24 \times 9 \times 8 \times 7} = \sqrt{12096}$$ 7. **Calculate the approximate value:** $$A \approx 109.95 \text{ square feet}$$ 8. **Calculate the lateral surface area:** $$\text{Lateral area} = P \times \text{length} = 48 \times 20 = 960 \text{ square feet}$$ 9. **Calculate total surface area:** $$\text{Surface Area} = 960 + 2 \times 109.95 = 960 + 219.9 = 1179.9 \text{ square feet}$$ 10. **Final answer:** $$\boxed{1179.9 \text{ square feet}}$$