The roof

The house's roof has the shape of a regular quadrilateral pyramid 5 m high and the edge of the base 7 m. How many tiles with an area of 540 cm² are needed?

Correct answer:

n =  1583

Step-by-step explanation:

$$\begin{gathered} h=5\text{m} \\ a=7\text{m} \\ {h}_2=\sqrt{(a/2{)}^2+h^2}=\sqrt{(7/2{)}^2+5^2}\doteq 6.1033\text{m} \\ {S}_1=\frac{a\cdot h_2}{2}=\frac{7\cdot 6.1033}{2}\doteq 21.3615{\text{m}}^2 \\ S=4\cdot S_1=4\cdot 21.3615=7\sqrt{149}{\text{m}}^2\doteq 85.4459{\text{m}}^2 \\ {S}_0=540{\text{cm}}^2\to {\text{m}}^2=540:10000{\text{m}}^2=0.054{\text{m}}^2 \\ {n}_1=S/S_0=85.4459/0.054\doteq 1582.3313 \\ n=\lceil n_1\rceil =\lceil 1582.3313\rceil =1583 \end{gathered}$$

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