Tower

The roof of the tower is a regular hexagonal pyramid with a base edge 5.7 meters long and a height 7 meters. How many m² of the sheet is required to cover the top of the tower? We must add 4% of metal for waste.

Final Answer:

S =  152 m²

Step-by-step explanation:

$$\begin{gathered} a=5.7\text{m} \\ v=7\text{m} \\ {a}^2-(a/2{)}^2=v_2^2 \\ {v}_2=a\cdot \frac{\sqrt{3}}{2}=5.7\cdot \frac{\sqrt{3}}{2}\doteq 4.9363\text{m} \\ {h}^2=v^2+v_2^2 \\ h=\sqrt{v^2+v_2^2}=\sqrt{7^2+4.9363^2}\doteq 8.5655\text{m} \\ {S}_1=\frac{1}{2}\cdot a\cdot h=\frac{1}{2}\cdot 5.7\cdot 8.5655\doteq 24.4116{\text{m}}^2 \\ q=100\%+4\%=1+\frac{4}{100}=1.04 \\ S=6\cdot S_1\cdot q=6\cdot 24.4116\cdot 1.04=152{\text{m}}^2 \end{gathered}$$

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