Box cardboard material

The closed box has the shape of a perpendicular prism with the base of an equilateral triangle. The edge of the base is 24 cm long, and the height of the box is 0.5 m. Calculate how many square meters of cardboard are needed to make 20 such boxes, assuming 5% of the material for bending.

Final Answer:

S =  8.6075 m²

Step-by-step explanation:

$$\begin{gathered} a=24\text{cm}\to \text{m}=24:100\text{m}=0.24\text{m} \\ h=0.5\text{m} \\ {S}_1=\frac{\sqrt{3}}{4}\cdot a^2=\frac{\sqrt{3}}{4}\cdot 0.24^2\doteq 0.0249{\text{m}}^2 \\ {S}_2=2\cdot S_1+3\cdot a\cdot h=2\cdot 0.0249+3\cdot 0.24\cdot 0.5\doteq 0.4099{\text{m}}^2 \\ q=100\%+5\%=1+\frac{5}{100}=1.05 \\ n=20 \\ S=q\cdot n\cdot S_2=1.05\cdot 20\cdot 0.4099=8.6075{\text{m}}^2 \end{gathered}$$

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