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!