Hexagon ABCDEF

In the regular hexagon ABCDEF, the diagonal AE has a length 8cm. Calculate the circumference and the hexagon area.

Correct answer:

o =  27.7128 cm
S =  55.4256 cm²

Step-by-step explanation:

$$\begin{gathered} u=8\text{ cm } \\ n=6 \\ A=360\mathrm{/}n=360\mathrm{/}6=60\text{ ° } \\ \sin A=u\mathrm{/}2:a \\ a={\displaystyle \frac{u}{2}}\mathrm{/}\sin A\mathrm{°}={\displaystyle \frac{u}{2}}\mathrm{/}\sin 60\mathrm{°}={\displaystyle \frac{8}{2}}\mathrm{/}\sin 60\mathrm{°}={\displaystyle \frac{8}{2}}\mathrm{/}0.866025=4.6188\text{ cm } \\ o=n\cdot a=6\cdot 4.6188=16\sqrt{3}=27.7128\text{ cm} \end{gathered}$$

$$\begin{gathered} S_1=a^2\cdot {\displaystyle \frac{\sqrt{3}}{4}}=4.6188^2\cdot {\displaystyle \frac{\sqrt{3}}{4}}\doteq 9.2376{\text{cm}}^2 \\ S=n\cdot S_1=6\cdot 9.2376=32\sqrt{3}=55.4256{\text{cm}}^2 \end{gathered}$$

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