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.(1 point)

The pentagon’s area is
square centimeters.

1 answer

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

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

First, let's calculate the perimeter of the pentagon. Since it has 5 sides, the perimeter \(P\) is:

\[ P = \text{side length} \times \text{number of sides} = 18 , \text{cm} \times 5 = 90 , \text{cm} \]

Now, substituting the perimeter and the apothem into the area formula:

\[ \text{Area} = \frac{1}{2} \times 90 , \text{cm} \times 12.4 , \text{cm} \]

Calculating the area:

\[ \text{Area} = \frac{1}{2} \times 90 \times 12.4 = 45 \times 12.4 = 558 , \text{cm}^2 \]

Thus, the area of the pentagon is \( \boxed{558} \) square centimeters.