Question

Use the formula to determine the area of a regular pentagon with edges measuring 4.5 inches and an apothem measuring 6 inches.

67.5
135
81
75

Answer 1

To calculate 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. Since the pentagon has 5 edges, each measuring 4.5 inches, the perimeter \( P \) is:

\[
P = 5 \times 4.5 = 22.5 \text{ inches}
\]

2. **Use the apothem** given as 6 inches.

3. **Plug the values into the area formula**:

\[
\text{Area} = \frac{1}{2} \times 22.5 \times 6
\]

\[
\text{Area} = \frac{1}{2} \times 135 = 67.5 \text{ square inches}
\]

Thus, the area of the regular pentagon is **67.5 square inches**.