1. **State the problem:** We need to find the surface area of a square pyramid with base side length $AD = CD = 1$ mm and triangular face height $EF = 8$ mm. 2. **Understand the shape:** The net of the square pyramid consists of one square base and four congruent triangular faces. 3. **Formula for surface area:** The surface area $S$ of a square pyramid is the sum of the base area and the areas of the four triangular faces: $$S = \text{Base area} + 4 \times \text{Area of one triangular face}$$ 4. **Calculate base area:** Since the base is a square with side length $1$ mm, $$\text{Base area} = 1 \times 1 = 1 \text{ mm}^2$$ 5. **Calculate area of one triangular face:** Each triangular face has base $1$ mm and height $EF = 8$ mm. Area of one triangle: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 1 \times 8 = 4 \text{ mm}^2$$ 6. **Calculate total area of four triangles:** $$4 \times 4 = 16 \text{ mm}^2$$ 7. **Calculate total surface area:** $$S = 1 + 16 = 17 \text{ mm}^2$$ **Final answer:** The surface area of the square pyramid is $17$ mm$^2$.