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 many m² roofing is required to cover the three walls of the sheathing, taking into account 40% of the additional coverage.

Correct result:

S =  49.5284 m²

Solution:

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

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