1. **State the problem:** Calculate the surface area of a square pyramid with base side length $6$ cm and slant height $7$ cm. 2. **Formula used:** The total 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 the base area $B$:** Since the base is a square with side length $6$ cm, $$B = 6^2 = 36 \text{ cm}^2$$ 4. **Calculate the lateral surface area $L$:** The lateral surface area is the sum of the areas of the four triangular faces. Each triangle has base $6$ cm and slant height $7$ cm. Area of one triangle: $$\frac{1}{2} \times 6 \times 7 = 21 \text{ cm}^2$$ 5. **Calculate total lateral area:** $$L = 4 \times 21 = 84 \text{ cm}^2$$ 6. **Calculate total surface area:** $$A = B + L = 36 + 84 = 120 \text{ cm}^2$$ **Final answer:** The surface area of the pyramid is $120$ cm$^2$.