1. **State the problem:** We need to find the surface area of a triangular prism with a triangular base having sides 7 m, 9 m, and a height of 3 m to the base 7 m, and the prism length (height) is 11 m. There is also a rectangle side of 4 m mentioned, but the main prism length is 11 m. 2. **Formula for surface area of a triangular prism:** The surface area (SA) is the sum of the areas of the two triangular bases plus the areas of the three rectangular faces. $$SA = 2 \times \text{Area of triangle base} + \text{Perimeter of triangle base} \times \text{length of prism}$$ 3. **Calculate the area of the triangular base:** The base of the triangle is 7 m and the height to this base is 3 m. $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 7 \times 3 = 10.5 \text{ m}^2$$ 4. **Calculate the perimeter of the triangular base:** The sides are 7 m, 9 m, and 4 m (the third side inferred from the rectangle side adjacent to the base). $$\text{Perimeter} = 7 + 9 + 4 = 20 \text{ m}$$ 5. **Calculate the lateral surface area:** Multiply the perimeter by the length of the prism (11 m): $$20 \times 11 = 220 \text{ m}^2$$ 6. **Calculate total surface area:** $$SA = 2 \times 10.5 + 220 = 21 + 220 = 241 \text{ m}^2$$ **Final answer:** The surface area of the triangular prism is **241 m²**.