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 result:

p =  4.8152 %

Solution:

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

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