Hip-roof

The roof consists of two isosceles trapezoids and two isosceles triangles. The roof plan is a rectangle with dimensions of 8m and 14m, and the roof ridge is 8m long. The height of the trapezoid is 5m, the height of the triangles is 4.2m. How many tiles are needed to cover the roof if 15 tiles are needed per 1m²?

Correct answer:

n =  2154

Step-by-step explanation:

$$\begin{gathered} a=8\text{m} \\ b=14\text{m} \\ h=8\text{m} \\ {v}_1=5\text{m} \\ {v}_2=4.2\text{m} \\ {S}_1=\frac{b+h}{2}\cdot v_1=\frac{14+8}{2}\cdot 5=55{\text{m}}^2 \\ {S}_2=\frac{a\cdot v_2}{2}=\frac{8\cdot 4.2}{2}=\frac{84}{5}=16\frac{4}{5}=16.8{\text{m}}^2 \\ S=2\cdot S_1+2\cdot S_2=2\cdot 55+2\cdot 16.8=\frac{718}{5}=143\frac{3}{5}=143.6 \\ n=15\cdot S=15\cdot 143.6=2154 \end{gathered}$$

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