1. **State the problem:** Find the surface area of a square pyramid with a square base side length of 6 cm and slant height of 10 cm. 2. **Formula for surface area of a square pyramid:** $$\text{Surface Area} = \text{Base Area} + \text{Lateral Area}$$ where $$\text{Base Area} = s^2$$ and $$\text{Lateral Area} = \frac{1}{2} \times \text{Perimeter} \times \text{Slant Height}$$ 3. **Calculate the base area:** $$s = 6 \text{ cm}$$ $$\text{Base Area} = 6^2 = 36 \text{ cm}^2$$ 4. **Calculate the perimeter of the base:** $$\text{Perimeter} = 4 \times 6 = 24 \text{ cm}$$ 5. **Calculate the lateral area:** $$\text{Lateral Area} = \frac{1}{2} \times 24 \times 10 = 12 \times 10 = 120 \text{ cm}^2$$ 6. **Calculate the total surface area:** $$\text{Surface Area} = 36 + 120 = 156 \text{ cm}^2$$ **Final answer:** - Square base area = 36 cm^2 - Triangular sides area = 120 cm^2 - Total surface area = 156 cm^2