1. **State the problem:** We need to find the surface area of a triangular prism with given side lengths. 2. **Identify the dimensions:** The triangular base has sides 5 m (height), 11 m (hypotenuse), and an unlabeled base side. The prism length (height of the rectangular sides) is 8 m. Other rectangular sides have lengths 9 m and 6 m, but these seem inconsistent with the prism length, so we focus on the given triangular base and prism length. 3. **Find the missing side of the triangle:** Using the Pythagorean theorem for the right triangle base: $$\text{base} = \sqrt{11^2 - 5^2} = \sqrt{121 - 25} = \sqrt{96} = 4\sqrt{6}$$ 4. **Calculate the area of the triangular base:** $$A_{triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 4\sqrt{6} \times 5 = 10\sqrt{6}$$ 5. **Calculate the perimeter of the triangular base:** $$P = 5 + 11 + 4\sqrt{6}$$ 6. **Calculate the lateral surface area:** $$A_{lateral} = P \times \text{length} = (5 + 11 + 4\sqrt{6}) \times 8 = 16 \times 8 + 4\sqrt{6} \times 8 = 128 + 32\sqrt{6}$$ 7. **Calculate total surface area:** $$A_{total} = 2 \times A_{triangle} + A_{lateral} = 2 \times 10\sqrt{6} + 128 + 32\sqrt{6} = 128 + 20\sqrt{6} + 32\sqrt{6} = 128 + 52\sqrt{6}$$ 8. **Final answer:** $$\boxed{128 + 52\sqrt{6} \text{ square meters}}$$ This is the surface area of the triangular prism.