Paper box

Calculate how much we'll pay for a three-side shaped prism box with a triangular base, and if it measures 12cm and 1.6dm, the hypotenuse measures 200mm. The box is 34cm high. We pay 0,13 € per square meter of paper.

Correct answer:

x =  2.37 Eur

Step-by-step explanation:

$$\begin{gathered} a=12\text{cm}\to \text{dm}=12:10\text{dm}=1.2\text{dm} \\ b=1.6\text{dm} \\ c=200\text{mm}\to \text{dm}=200:100\text{dm}=2\text{dm} \\ h=34\text{cm}\to \text{dm}=34:10\text{dm}=3.4\text{dm} \\ {S}_1=a\cdot b/2=1.2\cdot 1.6/2=\frac{24}{25}=0.96{\text{dm}}^2 \\ {S}_2=(a+b+c)\cdot h=(1.2+1.6+2)\cdot 3.4=\frac{408}{25}=16.32{\text{dm}}^2 \\ S=2\cdot S_1+S_2=2\cdot 0.96+16.32=\frac{456}{25}=18.24{\text{dm}}^2 \\ x=0.13\cdot S=0.13\cdot 18.24=2.37\text{Eur} \end{gathered}$$

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