Tower

The top of the tower is a regular hexagonal pyramid with base edge 8 meters long and a height 5 meters. How many m² of the sheet is required to cover the top of the tower if we count 8% of the sheet waste?

Correct result:

S =  221 m²

Solution:

$$\begin{gathered} a=8m \\ v=5m \\ {a}^2-(a\mathrm{/}2{)}^2=v_2^2 \\ {v}_2=a{\displaystyle \frac{\sqrt{3}}{2}}=6.928m \\ {h}^2=v^2+v_2^2 \\ h=\sqrt{5^2+6.928^2}=8.544m \\ {S}_1={\displaystyle \frac{1}{2}}ah={\displaystyle \frac{1}{2}}\cdot 8\cdot 8.544=34.18m^2 \\ S=6\cdot S_1\cdot (1+{\displaystyle \frac{8}{100}})=6\cdot 34.18\cdot 1.08=221{\text{m}}^2 \end{gathered}$$

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