Roof material calculation

The house's roof has the shape of a regular four-sided pyramid 4 m high with a base edge of 100 dm. We consider 30% of the roofing in addition to the overlap. Calculate how much m² of roofing is needed to cover the roof.

Final Answer:

S =  166.4812 m²

Step-by-step explanation:

$$\begin{gathered} h=4\text{m} \\ a=100\text{dm}\to \text{m}=100:10\text{m}=10\text{m} \\ q=100\%+30\%=1+\frac{30}{100}=1.3 \\ {w}^2=h^2+(a/2{)}^2 \\ w=\sqrt{h^2+(a/2{)}^2}=\sqrt{4^2+(10/2{)}^2}=\sqrt{41}\text{m}\doteq 6.4031\text{m} \\ {S}_1=\frac{a\cdot w}{2}=\frac{10\cdot 6.4031}{2}=5\sqrt{41}{\text{m}}^2\doteq 32.0156{\text{m}}^2 \\ S=4\cdot q\cdot S_1=4\cdot 1.3\cdot 32.0156=26\sqrt{41}=166.4812{\text{m}}^2 \end{gathered}$$

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