Question 63 - Problems - Chapter 1

Problem:

The roof of a house has a slope or pitch of 1:1 (that is 45°) The roof has a complex shape, with several gables and dormers (see the fig. below). The aerea of the ground floor is 250 $m^2$

Question:

What is the area of the roof surface?

Solution:

The slope of the roof at 45 ° is always the lower side divided by the cosine of the corner with the lower side.

The surface will therefore also be larger by a factor $cos(45°) = \frac{\sqrt{2}}{2}$.

$$ {\textrm{Surface}}_{\textrm{roof}} =\frac{{\textrm{Surface}}_{\textrm{ground}} }{\cos \left(45°\right)}\Rightarrow \frac{250\;m^2 }{\frac{\sqrt{2}}{2}}=\frac{2*250\;m^2 }{\sqrt{2}} $$

# Calculations
import numpy as np
Surface_house = 250
Surface_roof = (2 * Surface_house) / np.sqrt(2);
print(f'The surface of the roof is {Surface_roof:.0f} m2')

The surface of the roof is 354 m2