Question

Use the formula to determine the area of a regular pentagon with edges measuring 4.5 inches and an apothem measuring 6 inches.(1 point)
Responses

81 in.2
81 in. squared

67.5 in.2
67.5 in. squared

135 in.2
135 in. squared

75 in.2
75 in. squared

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**: The perimeter \(P\) is the sum of the lengths of all the edges. For a regular pentagon with each edge measuring 4.5 inches, the perimeter is:

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

2. **Use the Apothem**: The apothem is given as 6 inches.

3. **Calculate the Area**:

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

Now calculate:

\[
\text{Area} = \frac{1}{2} \times 22.5 \times 6 = \frac{1}{2} \times 135 = 67.5 \, \text{in}^2
\]

Thus, the area of the regular pentagon is **67.5 in²** (or **67.5 in squared**).

The correct response is:

**67.5 in.² or 67.5 in squared**.