The image you uploaded is of a square pyramid, and you are asked to determine both the lateral and total surface area.

Let's break it down step by step:

1. Lateral Surface Area: The lateral surface area of a square pyramid can be calculated using the formula:

   $A_{\text{lateral}} = \frac{1}{2} \times \text{Perimeter of base} \times \text{Slant height}$

   The perimeter of the base (which is a square) is calculated as:

   $\text{Perimeter} = 4 \times \text{side length}$

   The side length of the square base is given as $6 \, \text{cm}$, so:

   $\text{Perimeter} = 4 \times 6 = 24 \, \text{cm}$

   The slant height, as shown in the diagram, is $16 \, \text{cm}$.

   Now, we can calculate the lateral surface area:

   $A_{\text{lateral}} = \frac{1}{2} \times 24 \times 16 = 192 \, \text{cm}^2$

2. Total Surface Area: The total surface area includes the lateral surface area plus the area of the base. The area of the base is:

   $A_{\text{base}} = \text{side length}^2 = 6^2 = 36 \, \text{cm}^2$

   Therefore, the total surface area is:

   $A_{\text{total}} = A_{\text{lateral}} + A_{\text{base}} = 192 + 36 = 228 \, \text{cm}^2$

Final Answers:

• Lateral Surface Area = $192 \, \text{cm}^2$
• Total Surface Area = $228 \, \text{cm}^2$

Let me know if you'd like further clarification or details!

Here are some additional questions for your practice:

1. What is the formula for the volume of a square pyramid?
2. How would the lateral surface area change if the slant height was increased?
3. What is the relationship between the slant height and the height of a square pyramid?
4. How do you calculate the area of a triangle in the lateral surface area of a pyramid?
5. If the side length of the base was doubled, how would that affect the total surface area?

Tip: When working with geometric formulas, always make sure you’re using the correct measurements for each part of the shape (like slant height, base side, etc.). This ensures accurate calculations!