To solve for [tex]\( a \)[/tex] in the given formula for the area of a regular polygon, [tex]\( A = \frac{1}{2} a p \)[/tex], follow these steps:
1. Understand the formula: Recognize that the formula is [tex]\( A = \frac{1}{2} a p \)[/tex], where [tex]\( A \)[/tex] represents the area, [tex]\( a \)[/tex] represents the apothem (or perpendicular distance from the center to a side), and [tex]\( p \)[/tex] represents the perimeter of the polygon.
2. Multiply both sides by 2: To eliminate the fraction, multiply both sides of the equation by 2.
[tex]\[
2A = a p
\][/tex]
3. Isolate [tex]\( a \)[/tex]: To solve for [tex]\( a \)[/tex], divide both sides of the equation by [tex]\( p \)[/tex].
[tex]\[
a = \frac{2A}{p}
\][/tex]
This is the equation solved for [tex]\( a \)[/tex]. Therefore, the correct answer is:
[tex]\( a = \frac{2A}{p} \)[/tex]
From the given choices, this corresponds to:
- [tex]\( a = \frac{2A}{p} \)[/tex]
So, the correct option is:
[tex]\( \boxed{a = \frac{2A}{p}} \)[/tex]
