Classic tent

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

Correct result:

S =  10.5 m²
V =  2.7 m³

Solution:

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

$V=S_1\cdot l=1.35\cdot 2={\displaystyle \frac{27}{10}}={\displaystyle \frac{27}{10}}{\text{m}}^3=2.7{\text{m}}^3$

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