Question

What is the side length of a regular hexagon with area 100 square centimeters

Answer 1

well, we know is a hexagon, so it has 6 sides, HEXA = 6.

`\textit{Area of a regular polygon}\\\\ A=\cfrac{1}{4}ns^2\cdot cot\left( (180^o)/(n) \right)~~ \begin{cases} n=\textit{number of sides}\\ s=\textit{length of a side}\\[-0.5em] \hrulefill\\ A=100\\ n=6 \end{cases}\implies 100=\cfrac{1}{4}(6)s^2\cdot cot\left( (180^o)/(6) \right) \\\\\\ 400=6s^2\cdot cot(30^o)\implies 400=6s^2\cdot √(3)\implies \cfrac{400}{6√(3)}=s^2 \\\\\\ \sqrt{\cfrac{400}{6√(3)}}=s\implies 6.2\approx s`

Answer 2

area= about 6.2 cm

Explanation: