Hip-roof

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

Final 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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