I will analyze the uploaded image to check the surface area (SA) calculations. Let me extract the necessary details and verify the solution.

Extracted Information:

From the diagram and notes on the image:

• The pyramid has:
  • A square base with side length $5 \, \text{cm}$.
  • A slant height of $8 \, \text{cm}$.

The surface area (SA) formula for a square pyramid is: $SA = \text{Base Area} + \text{Lateral Area}$

1. Base Area: The area of the square base is: $\text{Base Area} = s^2 = 5^2 = 25 \, \text{cm}^2$

2. Lateral Area: Each triangular face has an area of: $\text{Triangle Area} = \frac{1}{2} \times \text{base} \times \text{slant height}$ For one triangular face: $\text{Triangle Area} = \frac{1}{2} \times 5 \times 8 = 20 \, \text{cm}^2$ Since there are 4 triangular faces: $\text{Lateral Area} = 4 \times 20 = 80 \, \text{cm}^2$

3. Total Surface Area: $SA = \text{Base Area} + \text{Lateral Area} = 25 + 80 = 105 \, \text{cm}^2$

Verification:

The calculation provided in the image appears to match this process, and the surface area is correctly calculated as 105 cm².

Do you need further explanation or details? Let me know!
Here are 5 related questions to explore further:

1. What is the formula for the volume of a square pyramid?
2. How would the surface area change if the base side length doubled?
3. What is the difference between lateral area and surface area for 3D objects?
4. How can we verify the slant height given other dimensions of the pyramid?
5. Can this process apply to pyramids with non-square bases?

Tip: Always double-check formulas to ensure units and dimensions align during geometry calculations!