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 135 in.2 135 in. squared 67.5 in.2 67.5 in. squared 75 in.2 75 in. squared 81 in.2

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. First, calculate the perimeter of the pentagon. Since it has 5 edges each measuring 4.5 inches:

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

2. Next, plug the perimeter and the apothem into the area formula. The apothem is given as 6 inches:

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

3. Calculate:

\[ \text{Area} = \frac{1}{2} \times 22.5 \times 6 = \frac{1}{2} \times 135 = 67.5 \text{ square inches} \]

Thus, the area of the regular pentagon is 67.5 in².

Therefore, the answer is 67.5 in.².