The roof

The roof of the tower has the shape of a regular quadrangular pyramid, the base edge of which is 11 m long and the side wall of the animal with the base an angle of 57°. Calculate how much roofing we need to cover the entire roof, if we count on 15% waste.

Correct answer:

x =  255.4903 m²

Step-by-step explanation:

$$\begin{gathered} a=11\text{ m } \\ \alpha =57^{\circ }\to \text{ rad}=57^{\circ }\cdot {\displaystyle \frac{\pi }{180}}=57^{\circ }\cdot {\displaystyle \frac{3.1415926}{180}}=0.99484=19\pi \mathrm{/}60 \\ q=15\mathrm{\%}=1+{\displaystyle \frac{15}{100}}=1.15 \\ \cos \alpha =a\mathrm{/}2:h_1 \\ {h}_1=a\mathrm{/}2\mathrm{/}\cos (\alpha )=11\mathrm{/}2\mathrm{/}\cos (0.9948)\doteq 10.0984\text{ m } \\ {S}_1={\displaystyle \frac{a\cdot h_1}{2}}={\displaystyle \frac{11\cdot 10.0984}{2}}\doteq 55.5414{\text{m}}^2 \\ x=4\cdot S_1\cdot q=4\cdot 55.5414\cdot 1.15=255.4903{\text{m}}^2 \end{gathered}$$

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