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=(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=(mp)/(2) \\ \downarrow \\ 2\cdot A=2\cdot(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 \\ (2A)/(m)=(mp)/(m) \\ \downarrow \\ (2A)/(m)=p \end{gathered}`

Answer- A: p = 2A/m