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.