Observation tower

An observation tower is covered with a roof in the shape of a regular quadrilateral pyramid with a base edge of 8 m and a height of 6 m. 60% of the roofing needs to be replaced. How many m² of new roofing material need to be bought?

Final Answer:

S =  69.23 m²

Step-by-step explanation:

$$\begin{gathered} a=8\text{m} \\ h=6\text{m} \\ {h}_2=\sqrt{h^2+(a/2{)}^2}=\sqrt{6^2+(8/2{)}^2}=2\sqrt{13}\text{m}\doteq 7.2111\text{m} \\ {S}_1=\frac{a\cdot h_2}{2}=\frac{8\cdot 7.2111}{2}=8\sqrt{13}{\text{m}}^2\doteq 28.8444{\text{m}}^2 \\ {S}_2=4\cdot S_1=4\cdot 28.8444=32\sqrt{13}{\text{m}}^2\doteq 115.3776{\text{m}}^2 \\ r=60\%=\frac{60}{100}=\frac{3}{5}=0.6 \\ S=r\cdot S_2=0.6\cdot 115.3776=69.23{\text{m}}^2 \end{gathered}$$

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