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.

Result

S =  49.528 m²

Solution:

$h=4 \ \text{m} \ \\ a=5 \ \text{m} \ \\ q=40 \%=1 + \dfrac{ 40 }{ 100 }=1.4 \ \\ \ \\ w^2=h^2+(a/2)^2 \ \\ w=\sqrt{ h^2+(a/2)^2 }=\sqrt{ 4^2+(5/2)^2 } \doteq 4.717 \ \text{m} \ \\ S_{1}=\dfrac{ a \cdot \ w }{ 2 }=\dfrac{ 5 \cdot \ 4.717 }{ 2 } \doteq 11.7925 \ \text{m}^2 \ \\ \ \\ S=3 \cdot \ q \cdot \ S_{1}=3 \cdot \ 1.4 \cdot \ 11.7925 \doteq 49.5284 \doteq 49.528 \ \text{m}^2$

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