Answer :
To find the area of a regular pentagon, you can use the formula for the area of a regular polygon:
[tex]A = \frac{1}{2} \times a \times P[/tex]
where:
- [tex]A[/tex] is the area of the pentagon.
- [tex]a[/tex] is the apothem (a line from the center to the middle of one of its sides, and perpendicular to the side).
- [tex]P[/tex] is the perimeter of the pentagon.
Given:
- The side length of the regular pentagon is 18 centimeters.
- The apothem is 12.4 centimeters.
To find the perimeter ([tex]P[/tex]), multiply the side length by the number of sides (since a pentagon has 5 sides):
[tex]P = 5 \times 18 = 90 \text{ centimeters}[/tex]
Now, substitute the values of [tex]a[/tex] and [tex]P[/tex] into the area formula:
[tex]A = \frac{1}{2} \times 12.4 \times 90[/tex]
Calculating the above expression:
[tex]A = 0.5 \times 12.4 \times 90 = 558 \text{ square centimeters}[/tex]
Therefore, the area of the pentagon is 558 square centimeters.
