The bus stop

The bus stop waiting room has the shape of a regular quadrilateral pyramid 4 m high with a 5 m base edge. Calculate how much m² roofing is required to cover the sheathing three walls, taking 40% of the additional coverage.

Correct answer:

S =  49.5284 m²

Step-by-step explanation:

$$\begin{gathered} h=4\text{m} \\ a=5\text{m} \\ q=40\%=1+\frac{40}{100}=1.4 \\ {w}^2=h^2+(a/2{)}^2 \\ w=\sqrt{h^2+(a/2{)}^2}=\sqrt{4^2+(5/2{)}^2}\doteq 4.717\text{m} \\ {S}_1=\frac{a\cdot w}{2}=\frac{5\cdot 4.717}{2}\doteq 11.7925{\text{m}}^2 \\ S=3\cdot q\cdot S_1=3\cdot 1.4\cdot 11.7925=49.5284{\text{m}}^2 \end{gathered}$$

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