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?

Question

kinggeorge · Answer

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 $P=23.25$

kinggeorge · Answer

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.