Question

A regular hexagon has perimeter 72m. Find the area

Answer 1

A regular hexagon has six equal sides:

If you notice, a regular hexagon has exactly six equilateral triangles inside of it.

So, to find the area we could find the area of a triangle and then multiply this result by 6. This seems to be a little bit complicated to do, so, there's a formula to find the area of a regular hexagon, which is:

`\begin{gathered} A=(3√(3)s^2)/(2) \\ Where: \\ s:Measure\text{ of a side of the regular hexagon} \end{gathered}`

We know that the measure of any side of our regular hexagon equals 12m, so, we could just replace in the equation:

`A=(3√(3)(12m)^2)/(2)\rightarrow A=(3√(3)(144m^2))/(2)\rightarrow A=216√(3)m^2`

Simplified, that's about 374.1 m2.