1. **State the problem:** Find the surface area of a square pyramid with side length $1$ ft and slant height $4$ ft. 2. **Formula for surface area of a square pyramid:** $$\text{Surface Area} = \text{Base Area} + \text{Lateral Area}$$ where $$\text{Base Area} = s^2$$ $$\text{Lateral Area} = 2 s l$$ Here, $s$ is the side length of the square base, and $l$ is the slant height. 3. **Calculate the base area:** $$s = 1$$ $$\text{Base Area} = 1^2 = 1$$ 4. **Calculate the lateral area:** $$l = 4$$ $$\text{Lateral Area} = 2 \times 1 \times 4 = 8$$ 5. **Calculate total surface area:** $$\text{Surface Area} = 1 + 8 = 9$$ 6. **Answer:** The surface area of the square pyramid is $9$ square feet.