1. **State the problem:** Find the missing height $h$ of a triangular prism given the surface area and dimensions of the base. 2. **Given:** - Base edges: 13 ft, 10 ft, 24 ft - Two rectangular faces with dimensions involving $h$ - Total surface area = 984 ft² 3. **Formula for surface area of a triangular prism:** $$\text{Surface Area} = \text{Perimeter of base} \times h + 2 \times \text{Area of triangular base}$$ 4. **Calculate the perimeter of the base:** $$P = 13 + 10 + 24 = 47 \text{ ft}$$ 5. **Calculate the area of the triangular base using Heron's formula:** - Semi-perimeter: $$s = \frac{47}{2} = 23.5$$ - Area: $$A = \sqrt{s(s-13)(s-10)(s-24)} = \sqrt{23.5(23.5-13)(23.5-10)(23.5-24)}$$ $$= \sqrt{23.5 \times 10.5 \times 13.5 \times (-0.5)}$$ Since one term is negative, this indicates the triangle is not valid with these sides, so we must assume the prism's lateral faces are rectangles with given dimensions. 6. **Assuming the lateral faces are rectangles with dimensions 13 ft by $h$, 10 ft by $h$, and 24 ft by $h$, the lateral surface area is:** $$L = (13 + 10 + 24)h = 47h$$ 7. **Calculate the area of the two triangular bases:** Since the problem does not provide the area of the base, we use the total surface area formula: $$\text{Surface Area} = L + 2 \times \text{Area of base} = 984$$ 8. **Rearranged to find $h$:** $$47h + 2A = 984$$ 9. **If the area of the base is unknown, we cannot solve for $h$ directly without it. However, if the problem expects $h$ to be found by subtracting the base areas from total surface area, then dividing by perimeter, we proceed as:** Assuming the base area is given or can be calculated, let’s denote it as $A$. $$47h = 984 - 2A$$ $$h = \frac{984 - 2A}{47}$$ Since $A$ is not provided, the problem cannot be solved further without additional information. **Final answer:** Cannot determine $h$ without the area of the triangular base.