Question

A regular pentagon has side lengths of 18 centimeters and an apothem of 12.4 centimeters. Use the formula to find the area of the pentagon

Answer 1

To find the area of a regular pentagon, you can use the formula:

\[
\text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem}
\]

1. **Calculate the perimeter of the pentagon**: The perimeter is the total length of all the sides. For a regular pentagon with side lengths of 18 centimeters, the perimeter \( P \) can be calculated as follows:

\[
P = 5 \times \text{side length} = 5 \times 18 = 90 \text{ cm}
\]

2. **Use the apothem provided**: The apothem (a) is given as 12.4 cm.

3. **Calculate the area**: Now, substitute the perimeter and apothem into the area formula:

\[
\text{Area} = \frac{1}{2} \times P \times a = \frac{1}{2} \times 90 \times 12.4
\]

Calculating this step-by-step:

\[
\text{Area} = \frac{1}{2} \times 90 = 45
\]

\[
\text{Area} = 45 \times 12.4 = 558
\]

Therefore, the area of the regular pentagon is

\[
\text{Area} = 558 \text{ cm}^2
\]