Hexagon area

The center of the regular hexagon is 21 cm away from its side. Calculate the hexagon side and its area.

Correct answer:

a =  24.2487 cm
S =  1527.6688 cm²

Step-by-step explanation:

$$\begin{gathered} h=21\text{ cm } \\ n=6 \\ a=h\cdot 2\mathrm{/}\sqrt{3}=21\cdot 2\mathrm{/}\sqrt{3}=14\sqrt{3}=24.2487\text{ cm} \end{gathered}$$

$$\begin{gathered} S_1={\displaystyle \frac{a\cdot h}{2}}={\displaystyle \frac{24.2487\cdot 21}{2}}=147\sqrt{3}{\text{cm}}^2\doteq 254.6115{\text{cm}}^2 \\ S=n\cdot S_1=6\cdot 254.6115=1527.6688{\text{cm}}^2 \end{gathered}$$

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