1. **State the problem:** We need to find the surface area of the salt shaker top, which is a square pyramid with base side length $AD = 20$ mm and slant height $EG = 7.76$ mm. 2. **Formula:** The surface area (SA) of a square 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 $AD = 20$ mm, $$B = AD^2 = 20^2 = 400 \text{ mm}^2$$ 4. **Calculate the perimeter $P$ of the base:** $$P = 4 \times AD = 4 \times 20 = 80 \text{ mm}$$ 5. **Use the given slant height $s = EG = 7.76$ mm.** 6. **Calculate the lateral surface area:** $$\frac{1}{2} P s = \frac{1}{2} \times 80 \times 7.76 = 40 \times 7.76 = 310.4 \text{ mm}^2$$ 7. **Calculate the total surface area:** $$SA = 310.4 + 400 = 710.4 \text{ mm}^2$$ **Final answer:** The surface area of the salt shaker top is **710.4 square millimeters**.