Quadrilateral 29201

How much sheet is needed for a roof with the shape of a regular quadrilateral pyramid if its edge is 2.8 m long and the height of the roof is 0.8 m? Calculate 10% for the overlap (extra).

Correct answer:

S =  9.9327 m²

Step-by-step explanation:

$$\begin{gathered} a=2.8\text{m} \\ h=0.8\text{m} \\ {h}_2=\sqrt{h^2+(a/2{)}^2}=\sqrt{0.8^2+(2.8/2{)}^2}\doteq 1.6125\text{m} \\ {S}_1=a\cdot h_2/2=2.8\cdot 1.6125/2\doteq 2.2574{\text{m}}^2 \\ {S}_2=4\cdot S_1=4\cdot 2.2574\doteq 9.0297{\text{m}}^2 \\ q=100\%+10\%=1+\frac{10}{100}=1.1 \\ S=S_2\cdot q=9.0297\cdot 1.1=9.9327{\text{m}}^2 \end{gathered}$$

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