Roof material

In the form of a pyramid with a square floor plan, the house's roof has dimensions of 12 x 12 m, at the highest point, a height of 2 m. How much roofing do we need to buy? Count on a 10% reserve.

Final Answer:

S =  166.9683 m²

Step-by-step explanation:

$$\begin{gathered} a=12\text{m} \\ h=2\text{m} \\ q=100\%+10\%=1+\frac{10}{100}=1.1 \\ {w}^2=h^2+(a/2{)}^2 \\ w=\sqrt{h^2+(a/2{)}^2}=\sqrt{2^2+(12/2{)}^2}=2\sqrt{10}\text{m}\doteq 6.3246\text{m} \\ {S}_1=\frac{a\cdot w}{2}=\frac{12\cdot 6.3246}{2}=12\sqrt{10}{\text{m}}^2\doteq 37.9473{\text{m}}^2 \\ S=4\cdot q\cdot S_1=4\cdot 1.1\cdot 37.9473=166.9683{\text{m}}^2 \end{gathered}$$

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