To find the area of a regular pentagon, where each side has a length of 7 cm, and the apothem is 8 cm, we can use the following steps:
1. Calculate the Perimeter:
- A regular pentagon has 5 sides.
- Each side has a length of 7 cm.
- Therefore, the perimeter (P) of the pentagon can be calculated as:
[tex]\[
P = \text{number of sides} \times \text{side length} = 5 \times 7 = 35 \text{ cm}
\][/tex]
2. Calculate the Area:
- The formula to find the area (A) of a regular polygon using the apothem (a) and perimeter is:
[tex]\[
A = \frac{1}{2} \times \text{perimeter} \times \text{apothem}
\][/tex]
- Substitute the values of the perimeter (35 cm) and the apothem (8 cm):
[tex]\[
A = \frac{1}{2} \times 35 \times 8 = \frac{1}{2} \times 280 = 140 \text{ cm}^2
\][/tex]
Thus, the area of the pentagon is 140 cm². None of the listed options match this answer exactly, so it seems there might have been an error in the provided options. However, based on our calculations, 140 cm² is the correct area of the pentagon.
