Roof 7

The roof has the shape of a regular quadrangular pyramid with a base edge of 12 m and a height of 4 m. How many percent is folds and waste if in construction was consumed 181.4m² of plate?

Correct answer:

p =  4.8152 %

Step-by-step explanation:

$$\begin{gathered} a=12\text{m} \\ h=4\text{m} \\ S=181.4{\text{m}}^2 \\ {h}_2=\sqrt{h^2+(a/2{)}^2}=\sqrt{4^2+(12/2{)}^2}=2\sqrt{13}\text{m}\doteq 7.2111\text{m} \\ {S}_1=h_2\cdot a/2=7.2111\cdot 12/2=12\sqrt{13}{\text{m}}^2\doteq 43.2666{\text{m}}^2 \\ {S}_2=4\cdot S_1=4\cdot 43.2666=48\sqrt{13}{\text{m}}^2\doteq 173.0665{\text{m}}^2 \\ p=100\cdot (S-S_2)/S_2=100\cdot (181.4-173.0665)/173.0665=4.8152\% \end{gathered}$$

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