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

Sagot :

tdamico25

Answer:

area= about 6.2 cm

Step-by-step explanation:

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

[tex]\textit{Area of a regular polygon}\\\\ A=\cfrac{1}{4}ns^2\cdot cot\left( \frac{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( \frac{180^o}{6} \right) \\\\\\ 400=6s^2\cdot cot(30^o)\implies 400=6s^2\cdot \sqrt{3}\implies \cfrac{400}{6\sqrt{3}}=s^2 \\\\\\ \sqrt{\cfrac{400}{6\sqrt{3}}}=s\implies 6.2\approx s[/tex]

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