Roof sheet calculation

Above the pavilion, with a square floor plan with side a = 12 m, is a pyramid-shaped roof with a height of 4.5 m. How many m² of sheet metal is needed to cover this roof?

Final Answer:

S =  180 m²

Step-by-step explanation:

$$\begin{gathered} a=12\text{m} \\ h=4.5\text{m} \\ {h}_2=\sqrt{(a/2{)}^2+h^2}=\sqrt{(12/2{)}^2+4.5^2}=\frac{15}{2}=7.5\text{m} \\ {S}_1=\frac{a\cdot h_2}{2}=\frac{12\cdot \frac{15}{2}}{2}=45{\text{m}}^2 \\ S=4\cdot S_1=4\cdot 45=180{\text{m}}^2 \end{gathered}$$

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