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------------------------------------------------ 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. The pentagon's area is __________ square centimeters.

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.

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