Hexagonal pyramid

Find the area of a shell of the regular hexagonal pyramid if you know that its base edge is 5 cm long and the height of this pyramid is 10 cm.

Correct answer:

S =  163.4587 cm²

Step-by-step explanation:

$$\begin{gathered} a=5\text{cm} \\ v=10\text{cm} \\ n=6 \\ {v}_2=\sqrt{3}/2\cdot a=\sqrt{3}/2\cdot 5\doteq 4.3301\text{cm} \\ {v}_3=\sqrt{v^2+v_2^2}=\sqrt{10^2+4.3301^2}\doteq 10.8972\text{cm} \\ {S}_1=\frac{a\cdot v_3}{2}=\frac{5\cdot 10.8972}{2}\doteq 27.2431{\text{cm}}^2 \\ S=n\cdot S_1=6\cdot 27.2431=163.4587{\text{cm}}^2 \end{gathered}$$

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