1. **State the problem:** We need to find the surface area of a triangular prism with a right triangle base where the legs are 7 m and 4 m, the hypotenuse is 9 m, and the prism height (length) is 11 m. 2. **Formula for surface area of a triangular prism:** The surface area $SA$ is given by: $$SA = 2 \times \text{Area of triangular base} + \text{Perimeter of base} \times \text{Height of prism}$$ 3. **Calculate the area of the triangular base:** Since the base is a right triangle with legs 7 m and 4 m, $$\text{Area} = \frac{1}{2} \times 7 \times 4 = 14 \text{ m}^2$$ 4. **Calculate the perimeter of the triangular base:** $$\text{Perimeter} = 7 + 4 + 9 = 20 \text{ m}$$ 5. **Calculate the lateral surface area:** $$\text{Lateral area} = \text{Perimeter} \times \text{Height} = 20 \times 11 = 220 \text{ m}^2$$ 6. **Calculate total surface area:** $$SA = 2 \times 14 + 220 = 28 + 220 = 248 \text{ m}^2$$ **Final answer:** The surface area of the triangular prism is $248$ square meters.