Roof cover

Above the pavilion with a square ground plan with a side length of a = 12 m is a pyramid-shaped roof with a height v = 4.5 m. Calculate how much m² of sheet metal is needed to cover this roof; if 5.5% of the sheet, we must add for joints and waste.

Correct answer:

S =  189.9 m²

Step-by-step explanation:

$$\begin{gathered} a=12\text{m} \\ v=4.5\text{m} \\ q=1+\frac{5.5}{100}=\frac{211}{200}=1.055 \\ {h}_2=\sqrt{v^2+(a/2{)}^2}=\sqrt{4.5^2+(12/2{)}^2}=\frac{15}{2}=7.5\text{m} \\ {S}_1=a\cdot h_2/2=12\cdot \frac{15}{2}/2=45{\text{m}}^2 \\ {S}_2=4\cdot S_1=4\cdot 45=180{\text{m}}^2 \\ S=S_2\cdot q=180\cdot \frac{211}{200}=\frac{180\cdot 211}{200}=\frac{37980}{200}=\frac{1899}{10}{\text{m}}^2=189.9{\text{m}}^2 \end{gathered}$$

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