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 result:

S =  189.9 m²

Solution:

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

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