Classic tent

The tent is shaped like a triangular prism. The front and rear walls are isosceles triangles with a height of 18 dm and arms 19.5 dm long. It is 1.5 m wide and 2 m long. How many square meters of fabric are needed to make a tent? How much air is in it?

Correct answer:

S =  10.5 m²
V =  2.7 m³

Step-by-step explanation:

$$\begin{gathered} v=18\text{dm}\to \text{m}=18:10\text{m}=1.8\text{m} \\ r=19.5\text{dm}\to \text{m}=19.5:10\text{m}=1.95\text{m} \\ a=1.5\text{m} \\ l=2\text{m} \\ {S}_1=\frac{v\cdot a}{2}=\frac{1.8\cdot 1.5}{2}=\frac{27}{20}=1.35{\text{m}}^2 \\ S=2\cdot S_1+2\cdot r\cdot l=2\cdot \frac{27}{20}+2\cdot \frac{39}{20}\cdot 2=\frac{21}{2}{\text{m}}^2=10.5{\text{m}}^2 \end{gathered}$$

$V=S_1\cdot l=\frac{27}{20}\cdot 2=\frac{27\cdot 2}{20}=\frac{54}{20}=2.7{\text{m}}^3$

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