To find the surface area of the square pyramid shown in the image, we calculate the area of the base and the four triangular faces.

Given Data:

• Side length of the square base, $s = 8$
• Slant height of each triangular face, $l = 6$

Steps:

1. Calculate the area of the base: $\text{Base area} = s^2 = 8^2 = 64$

2. Calculate the area of one triangular face: The formula for the area of a triangle is: $\text{Area of one triangular face} = \frac{1}{2} \times \text{base of triangle} \times \text{slant height}$ Here, the base of the triangle is the side length of the square base: $\text{Area of one triangular face} = \frac{1}{2} \times 8 \times 6 = 24$

3. Calculate the total area of the four triangular faces: $\text{Total triangular face area} = 4 \times 24 = 96$

4. Calculate the total surface area of the pyramid: $\text{Surface area} = \text{Base area} + \text{Total triangular face area}$ Substituting the values: $\text{Surface area} = 64 + 96 = 160$

Final Answer:

The surface area of the square pyramid is: $\boxed{160 \ \text{square units}}$

Would you like a detailed explanation of any step or more examples? Here are five related questions you might find helpful:

1. How do you find the slant height if only the perpendicular height is given?
2. What would the surface area be if the slant height increased by 2 units?
3. How do you calculate the volume of a square pyramid?
4. Can you find the surface area of a triangular pyramid using a similar method?
5. What happens to the surface area if the side length of the base doubles?

Tip: For pyramids, ensure you differentiate between slant height and perpendicular height before calculations!