To find the surface area of a square pyramid, we need to calculate the sum of the areas of its base and its four triangular faces.

Formula for Surface Area of a Square Pyramid:

$\text{Surface Area} = \text{Base Area} + \text{Lateral Area}$ Where:

• Base Area is the area of the square base: $A_{\text{base}} = s^2$ (where $s$ is the side length of the base).
• Lateral Area is the combined area of the four triangular faces: $A_{\text{lateral}} = 2 \cdot s \cdot l$ (where $l$ is the slant height of the pyramid).

Step 1: Calculate Base Area

$A_{\text{base}} = s^2 = 5^2 = 25 \, \text{in}^2$

Step 2: Calculate Lateral Area

$A_{\text{lateral}} = 2 \cdot s \cdot l = 2 \cdot 5 \cdot 5 = 50 \, \text{in}^2$

Step 3: Calculate Total Surface Area

$\text{Surface Area} = A_{\text{base}} + A_{\text{lateral}} = 25 + 50 = 75 \, \text{in}^2$

Thus, the surface area of the square pyramid is 75 square inches.

Would you like more details or have any questions?

Here are 5 related questions:

1. What is the surface area if the side length is doubled but the slant height remains the same?
2. How would the volume of the pyramid be calculated with the given dimensions?
3. What would the lateral area be if the slant height were increased to 6 inches?
4. How does the surface area change if both the base side length and slant height increase by 2 inches?
5. Can you explain how the Pythagorean theorem relates to finding the slant height of a pyramid?

Tip: Remember that the slant height is the distance from the top of the pyramid to the midpoint of one of the base's sides, not the height along the pyramid's vertical axis!