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 answer:

S =  10.5 m²
V =  2.7 m³

Step-by-step explanation:

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

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

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