Pyramid roof

How many m² of the galvanized sheet is used to cover the roof of the tower, which has the shape of a four-sided pyramid, whose base edge is 6 m long? The height of the tower is 9 m. When covering, is 5% metal waste expected?

Final Answer:

S =  119.5341 m²

Step-by-step explanation:

$$\begin{gathered} a=6\text{m} \\ h=9\text{m} \\ {h}_2=\sqrt{h^2+(a/2{)}^2}=\sqrt{9^2+(6/2{)}^2}=3\sqrt{10}\text{m}\doteq 9.4868\text{m} \\ {S}_1=\frac{h_2\cdot a}{2}=\frac{9.4868\cdot 6}{2}=9\sqrt{10}{\text{m}}^2\doteq 28.4605{\text{m}}^2 \\ {S}_2=4\cdot S_1=4\cdot 28.4605=36\sqrt{10}{\text{m}}^2\doteq 113.842{\text{m}}^2 \\ q=100\%+5\%=1+\frac{5}{100}=1.05 \\ S=q\cdot S_2=1.05\cdot 113.842=119.5341{\text{m}}^2 \end{gathered}$$

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