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?

Result

S =  13.093 m²
V =  2.4 m³

Solution:

$a=2 \ \text{m} \ \\ h=1.8 \ \text{m} \ \\ \ \\ s=\sqrt{ h^2+(a/2)^2 }=\sqrt{ 1.8^2+(2/2)^2 } \doteq 2.0591 \ \text{m} \ \\ S_{1}=a \cdot \ s/2=2 \cdot \ 2.0591/2 \doteq 2.0591 \ \text{m}^2 \ \\ S=1.07 \cdot \ (a^2+4 \cdot \ S_{1})=1.07 \cdot \ (2^2+4 \cdot \ 2.0591) \doteq 13.0931 \doteq 13.093 \ \text{m}^2$

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

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