1. **State the problem:** We need to find the surface area of a square-based pyramid where the base edges are 6 cm and each triangular face has a height of 19 cm. 2. **Formula for surface area of a square-based pyramid:** $$\text{Surface Area} = \text{Base Area} + \text{Lateral Area}$$ where - Base Area = area of the square base - Lateral Area = sum of the areas of the four triangular faces 3. **Calculate the base area:** The base is a square with side length 6 cm. $$\text{Base Area} = 6 \times 6 = 36 \text{ cm}^2$$ 4. **Calculate the area of one triangular face:** Each triangular face has a base of 6 cm and height 19 cm. $$\text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 6 \times 19 = 3 \times 19 = 57 \text{ cm}^2$$ 5. **Calculate the lateral area:** There are 4 identical triangular faces. $$\text{Lateral Area} = 4 \times 57 = 228 \text{ cm}^2$$ 6. **Calculate total surface area:** $$\text{Surface Area} = 36 + 228 = 264 \text{ cm}^2$$ **Final answer:** The surface area of the pyramid is $264$ cm$^2$.