1. **State the problem:** Calculate the surface area and volume of a 3D triangular prism-like solid with given edges: 10 ft, 13 ft, 8 ft, 9 ft, and height 7.6 ft. 2. **Identify the shape and given dimensions:** - The prism has a triangular base with sides 10 ft, 13 ft, and 9 ft. - The height (length) of the prism is 7.6 ft. - The 8 ft edge is likely the height of the triangular base (perpendicular from base to opposite vertex). 3. **Formulas:** - Volume of prism: $$V = \text{Area of base} \times \text{height}$$ - Surface area of prism: $$SA = 2 \times \text{Area of base} + \text{Perimeter of base} \times \text{height}$$ 4. **Calculate the area of the triangular base:** Using base = 9 ft and height = 8 ft, $$\text{Area} = \frac{1}{2} \times 9 \times 8 = 36 \text{ ft}^2$$ 5. **Calculate the perimeter of the triangular base:** $$P = 10 + 13 + 9 = 32 \text{ ft}$$ 6. **Calculate the volume:** $$V = 36 \times 7.6 = 273.6 \text{ ft}^3$$ 7. **Calculate the surface area:** $$SA = 2 \times 36 + 32 \times 7.6 = 72 + 243.2 = 315.2 \text{ ft}^2$$ **Final answers:** - Volume = $273.6$ ft$^3$ - Surface Area = $315.2$ ft$^2$