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To solve this problem of calculating the lateral area of a regular pentagonal pyramid, let's go through the steps once again.

### Steps to Solve:

1. **Determine the slant height (s):**
   - Given: \( s = 12 \, \text{cm} \).

2. **Calculate the perimeter of the base (P):**
   - The base is a regular pentagon with each side length \( a = 5 \, \text{cm} \).
   - The perimeter \( P \) is:
     \[
     P = 5 \times 5 \, \text{cm} = 25 \, \text{cm}
     \]

3. **Calculate the lateral area (A_L):**
   - The lateral area of a pyramid is given by the formula:
     \[
     A_L = \frac{1}{2} \times P \times s
     \]
   - Plugging in the values:
     \[
     A_L = \frac{1}{2} \times 25 \, \text{cm} \times 12 \, \text{cm}
     \]
   - Simplifying this:
     \[
     A_L = \frac{1}{2} \times 300 \, \text{cm}^2 = 150 \, \text{cm}^2
     \]

Therefore, the lateral area of the given regular pentagonal pyramid is \( 150 \, \text{cm}^2 \).

Would you like more details or have any questions? Here are 5 more questions you can ask:

1. How do you calculate the total surface area of a pyramid?
2. What is the volume formula for a pentagonal pyramid?
3. Can you explain how to find the slant height if it's not given?
4. How do you derive the perimeter of different polygonal bases?
5. Can you explain the concept of the apothem in relation to pyramids?

**Tip:** When working with pyramids, always identify and separate the components of the base and the lateral faces to simplify the calculations.

Learn how to calculate the lateral area of a regular pentagonal pyramid with a detailed step-by-step guide. This problem involves geometric concepts such as pyramids, perimeter calculation, and area computation. Suitable for high school students.

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