The formula for the area of a regular polygon is [tex]A=\frac{1}{2} a p[/tex]. What is the equation solved for [tex]a[/tex]?

A. [tex]a=2A[/tex]
B. [tex]a=2A-p[/tex]
C. [tex]a=\frac{2p}{A}[/tex]
D. [tex]a=\frac{2A}{p}[/tex]



Answer :

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.