Paper box

Calculate the paper consumption on the box-shaped quadrangular prism with rhombic footstall, base edge a=6 cm, and the adjacent base edges form an angle alpha = 60 °. The box height is 10 cm. How much m² of the paper is consumed 100 such boxes?

Final Answer:

S =  3.0235 m²

Step-by-step explanation:

$$\begin{gathered} a=6\text{cm} \\ \alpha =60{}^{\circ } \\ h=10\text{cm} \\ n=100 \\ o=4\cdot a=4\cdot 6=24\text{cm} \\ {S}_1=o\cdot h=24\cdot 10=240{\text{cm}}^2 \\ {S}_2=a^2\cdot \sin \alpha =a^2\cdot \sin 60°=6^2\cdot \sin 60°=6^2\cdot 0.866025=31.17691{\text{cm}}^2 \\ {S}_3=n\cdot (S_1+2\cdot S_2)=100\cdot (240+2\cdot 31.1769)\doteq 30235.3829{\text{cm}}^2 \\ S=S_3\to {\text{m}}^2=S_3:10000{\text{m}}^2=30235.3829:10000{\text{m}}^2=3.024{\text{m}}^2=3.0235{\text{m}}^2 \end{gathered}$$

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