1. **State the problem:** We need to find the surface area of a triangular pyramid composed of six triangular faces, with three top triangles each having height 11 ft and three bottom triangles with sides 7 ft and height 6.1 ft. 2. **Identify the triangles:** The pyramid has 6 triangular faces: 3 top triangles with height 11 ft and base 7 ft, and 3 bottom triangles with base 7 ft and height 6.1 ft. 3. **Formula for the area of a triangle:** $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ 4. **Calculate the area of one top triangle:** $$\text{Area}_{top} = \frac{1}{2} \times 7 \times 11 = \frac{1}{2} \times 77 = 38.5$$ 5. **Calculate the area of one bottom triangle:** $$\text{Area}_{bottom} = \frac{1}{2} \times 7 \times 6.1 = \frac{1}{2} \times 42.7 = 21.35$$ 6. **Calculate total surface area:** $$\text{Total area} = 3 \times 38.5 + 3 \times 21.35 = 115.5 + 64.05 = 179.55$$ 7. **Final answer:** The surface area of the triangular pyramid is $$179.55\ \text{ft}^2$$