Question

A regular pentagon has an apothem of 3.2 m and an area of 37.2 m². What is the length of one side of the pentagon?

Answer 1

The formula for finding the area of a regular pentagon is\[A={1 \over2}\cdot P\cdot a\]Where \(P\) is the total perimeter, and \(a\) is the length of the apothem. So you get the equation. \[37.2={1 \over2}\cdot P \cdot3.2\]If we solve for \(P\), we find that \(P=23.25\)

Answer 2

Now we need to find the length of a single side. A regular pentagon has 5 sides of the same length, so we can just divide \(P\) be 5 to get our answer.\[{23.25\over5}=4.65\]Would therefore be the length of a single side.