1. **State the problem:** Find the surface area of a square pyramid with base side length $1$ ft and slant height $5$ ft. 2. **Formula:** The surface area $A$ of a square pyramid is given by: $$A = B + L$$ where $B$ is the area of the square base and $L$ is the lateral surface area. 3. **Calculate base area:** Since the base is a square with side length $s=1$ ft, $$B = s^2 = 1^2 = 1 \text{ ft}^2$$ 4. **Calculate lateral area:** The lateral area is the sum of the areas of the four triangular faces. Each triangle has base $s=1$ ft and height equal to the slant height $l=5$ ft. Area of one triangle: $$\frac{1}{2} \times s \times l = \frac{1}{2} \times 1 \times 5 = \frac{5}{2} = 2.5 \text{ ft}^2$$ Since there are 4 triangles: $$L = 4 \times 2.5 = 10 \text{ ft}^2$$ 5. **Total surface area:** $$A = B + L = 1 + 10 = 11 \text{ ft}^2$$ **Final answer:** The surface area of the square pyramid is $11$ ft².