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 result:

x =  2.37 Eur

Solution:

$$\begin{gathered} a=12\text{ cm}\to \text{ dm}=12\mathrm{/}10\text{ dm}=1.2\text{ dm } \\ b=1.6\text{ dm } \\ c=200\text{ mm}\to \text{ dm}=200\mathrm{/}100\text{ dm}=2\text{ dm } \\ h=34\text{ cm}\to \text{ dm}=34\mathrm{/}10\text{ dm}=3.4\text{ dm } \\ {S}_1=a\cdot b\mathrm{/}2=1.2\cdot 1.6\mathrm{/}2={\displaystyle \frac{24}{25}}=0.96{\text{dm}}^2 \\ {S}_2=(a+b+c)\cdot h=(1.2+1.6+2)\cdot 3.4={\displaystyle \frac{408}{25}}=16.32{\text{dm}}^2 \\ S=2\cdot S_1+S_2=2\cdot 0.96+16.32={\displaystyle \frac{456}{25}}=18.24{\text{dm}}^2 \\ x=0.13\cdot S=0.13\cdot 18.24={\displaystyle \frac{1482}{625}}={\displaystyle \frac{1482}{625}}\text{ Eur}=2.37\text{ Eur} \end{gathered}$$

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