To find the area of a regular pentagon with a given apothem and side length, you can follow these steps:
1. Identify the number of sides: A pentagon has 5 sides.
2. Calculate the perimeter: The perimeter [tex]\( P \)[/tex] of a pentagon can be calculated by multiplying the number of sides [tex]\( n \)[/tex] by the length of one side [tex]\( s \)[/tex].
[tex]\[
P = n \times s
\][/tex]
Substituting the given values:
[tex]\[
P = 5 \times 8.7 \text{ inches} = 43.5 \text{ inches}
\][/tex]
3. Use the formula to find the area: The area [tex]\( A \)[/tex] of a regular polygon can be found using the formula:
[tex]\[
A = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem}
\][/tex]
Substituting the perimeter and the given apothem:
[tex]\[
A = \frac{1}{2} \times 43.5 \text{ inches} \times 6 \text{ inches}
\][/tex]
4. Calculate the area:
[tex]\[
A = \frac{1}{2} \times 43.5 \times 6 = 130.5 \text{ square inches}
\][/tex]
Therefore, the area of the regular pentagon is [tex]\( 130.5 \)[/tex] square inches.
