https://file.aiquickdraw.com/mathbot/file/1729911463904dq5y1jph.jpg

The image shows a **regular pentagon**, and the problem asks for its **area**. We are given:

- The **apothem** (distance from the center to a side) = 2.1 cm  
- The **side length** = 3 cm  

### Formula for the area of a regular pentagon:
\[
A = \frac{1}{2} \times P \times a
\]
where:
- \(P\) = Perimeter of the pentagon  
- \(a\) = Apothem  

### Step-by-Step Solution:

1. **Calculate the perimeter \(P\)**:
   Since the pentagon has 5 equal sides:
   \[
   P = 5 \times 3 = 15 \, \text{cm}
   \]

2. **Apply the area formula**:
   \[
   A = \frac{1}{2} \times 15 \times 2.1
   \]
   \[
   A = \frac{1}{2} \times 31.5 = 15.75 \, \text{cm}^2
   \]

### Final Answer:
\[
A = 15.75 \, \text{cm}^2
\]

So, the correct option is:
\[
\boxed{15.75 \, \text{cm}^2}
\]

Do you have any further questions or need clarification?  

---

Here are 5 related questions you might explore:
1. What is the general formula for the area of any regular polygon?
2. How does the apothem help in calculating the area of polygons?
3. What is the relationship between apothem and radius in regular polygons?
4. How would the area change if the side length were doubled?
5. Can this method apply to irregular pentagons?

**Tip:** The apothem simplifies area calculations by dividing the polygon into congruent triangles!

Find the area of a regular pentagon with an apothem of 2.1 cm and side length of 3 cm.

Learn how to calculate the area of a regular pentagon given an apothem of 2.1 cm and side length of 3 cm. This solution includes step-by-step calculations using the formula for regular polygons. Suitable for students in Grades 8-10.

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