Question

The formula for the area, A, of a regular polygon is A = 1/2mp, where m is the apothem, and p is the perimeter. Which formula can be used to determine p, given A and m?

Answer 1

Solving an equation

Initial explanation

We want to solve the equation:

$A=\frac{mp}{2}$

for p.

In order to do so, we want to "leave alone" p on the right side of the equation. The only rule we need to follow is

So, we are going to leave p alone on the right side of the equal.

Step 1- taking 2 to the left side

We multiply both sides by 2:

$\begin{gathered} A=\frac{mp}{2} \\ \downarrow \\ 2\cdot A=2\cdot\frac{mp}{2} \\ \downarrow \\ 2A=mp \end{gathered}$

Step 2- taking m to the left side

We divide both sides by m:

$\begin{gathered} 2A=mp \\ \downarrow \\ \frac{2A}{m}=\frac{mp}{m} \\ \downarrow \\ \frac{2A}{m}=p \end{gathered}$

Answer- A: p = 2A/m