Question

A regular hexagon has a perimeter of 70 m. Find its area. Leave your answer in simplest radical form.

Answer 1

A HEXA=6, gon, has 6 sides, and we know the perimeter, all sides added up, is 70, so one side is just 70/6, or 35/3

$\bf \textit{area of a polygon}\\\\ A=\cfrac{1}{4}ns^2\ cot\left( \frac{180}{n} \right)\qquad \begin{cases} n=\textit{number of sides}\\ s=\textit{length of one side}\\ \frac{180}{n}=\textit{angle in degrees}\\ ----------\\ n=6\\ s=\frac{35}{3} \end{cases} \\\\\\ A=\cfrac{1}{4}\cdot 6\cdot \left( \frac{35}{3} \right)^2\cdot ot\left( \frac{180}{6} \right)$