Roof cardboard

The roof of the prefabricated holiday cottage has the shape of a regular quadrilateral pyramid with a length of the base edge of 8 meters and a height of 9 m. How many square meters of cardboard are needed to cover the roof?

Final Answer:

S =  157.5817 m²

Step-by-step explanation:

$$\begin{gathered} a=8\text{m} \\ h=9\text{m} \\ {h}_2=\sqrt{h^2+(a/2{)}^2}=\sqrt{9^2+(8/2{)}^2}=\sqrt{97}\text{m}\doteq 9.8489\text{m} \\ {S}_1=a\cdot h_2/2=8\cdot 9.8489/2=4\sqrt{97}{\text{m}}^2\doteq 39.3954{\text{m}}^2 \\ S=4\cdot S_1=4\cdot 39.3954=16\sqrt{97}=157.5817{\text{m}}^2 \end{gathered}$$

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