Decimeters 2551

The cardboard packaging without a lid has the shape of a regular hexagonal prism with a main edge that is 12 cm long and 15 cm high. How much cardboard is used to make five packages if 10% of the cardboard is added for folds? Give results in square decimeters and rounded to units.

Final Answer:

x =  80 dm²

Step-by-step explanation:

$$\begin{gathered} a=12\text{cm} \\ h=15\text{cm} \\ n=5 \\ q=100\%+10\%=1+\frac{10}{100}=1.1 \\ {S}_1=\frac{\sqrt{3}}{4}\cdot a^2=\frac{\sqrt{3}}{4}\cdot 12^2=36\sqrt{3}{\text{cm}}^2\doteq 62.3538{\text{cm}}^2 \\ {S}_2=a\cdot h=12\cdot 15=180{\text{cm}}^2 \\ {S}_3=6\cdot (S_1+S_2)=6\cdot (62.3538+180)\doteq 1454.123{\text{cm}}^2 \\ {S}_4=S_3\to {\text{dm}}^2=S_3:100{\text{dm}}^2=1454.123:100{\text{dm}}^2=14.54123{\text{dm}}^2 \\ x=n\cdot q\cdot S_4=5\cdot 1.1\cdot 14.5412=80{\text{dm}}^2 \end{gathered}$$

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