Sure, let's solve this step by step:
The given formula for the area of a regular polygon is:
[tex]\[ A = \frac{1}{2} \times a \times p \][/tex]
where \( A \) is the area, \( a \) is the apothem, and \( p \) is the perimeter.
We need to solve this formula for \( a \). Follow these steps:
1. Start with the given formula:
[tex]\[ A = \frac{1}{2} \times a \times p \][/tex]
2. To isolate \( a \), first eliminate the fraction by multiplying both sides of the equation by 2:
[tex]\[ 2A = a \times p \][/tex]
3. Now, solve for \( a \) by dividing both sides of the equation by \( p \):
[tex]\[ a = \frac{2A}{p} \][/tex]
Therefore, the equation solved for \( a \) is:
[tex]\[ a = \frac{2A}{p} \][/tex]
Among the given choices, the correct formula is:
[tex]\[ a = \frac{2A}{p} \][/tex]
The correct choice is the fourth option.
