1. **State the problem:** We need to find the surface area of a square pyramid with base side length $AD = 18.7$ feet and slant height $EG = 25.71$ feet. 2. **Formula for surface area:** The surface area $SA$ of a pyramid is given by $$SA = \frac{1}{2} P s + B$$ where $P$ is the perimeter of the base, $s$ is the slant height, and $B$ is the area of the base. 3. **Calculate the area of the base $B$:** Since the base is a square with side length $AD = 18.7$ feet, $$B = AD^2 = 18.7^2 = 349.69 \text{ square feet}$$ 4. **Calculate the perimeter $P$ of the base:** The perimeter of a square is $$P = 4 \times AD = 4 \times 18.7 = 74.8 \text{ feet}$$ 5. **Use the given slant height $s = EG = 25.71$ feet.** 6. **Calculate the lateral surface area:** $$\frac{1}{2} P s = \frac{1}{2} \times 74.8 \times 25.71$$ Intermediate step showing cancellation: $$= \frac{\cancel{1}}{\cancel{2}} \times 74.8 \times 25.71 = 37.4 \times 25.71 = 961.554 \text{ square feet}$$ 7. **Calculate total surface area:** $$SA = 961.554 + 349.69 = 1311.244 \text{ square feet}$$ **Final answer:** The surface area of the pyramid is approximately **1311.24 square feet**.