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:

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

Try another example