The tent

The tent shape of a regular quadrilateral pyramid has a base edge length a = 2 m and a height v = 1.8 m. How many m² of cloth we need to make the tent if we have to add 7% of the seams? How many m³ of air will be in the tent?

Correct result:

S =  13.0931 m²
V =  2.4 m³

Solution:

$$\begin{gathered} a=2\text{ m } \\ h=1.8\text{ m } \\ s=\sqrt{h^2+(a\mathrm{/}2{)}^2}=\sqrt{1.8^2+(2\mathrm{/}2{)}^2}\doteq 2.0591\text{ m } \\ {S}_1=a\cdot s\mathrm{/}2=2\cdot 2.0591\mathrm{/}2\doteq 2.0591{\text{m}}^2 \\ S=1.07\cdot (a^2+4\cdot S_1)=1.07\cdot (2^2+4\cdot 2.0591)=13.0931{\text{m}}^2 \end{gathered}$$

$V=a^2\cdot h\mathrm{/}3=2^2\cdot 1.8\mathrm{/}3={\displaystyle \frac{12}{5}}={\displaystyle \frac{12}{5}}{\text{m}}^3=2.4{\text{m}}^3$

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