Box

The cardboard is a box-shaped quadrangular prism with a rhombic base. Rhombus has a side 5 cm, one diagonal 8 cm long, and the box's height is 12 cm. The package will open at the top.

How many cm² of cardboard do we need to cover overlap and joints that are 5% of the area of cardboard?

Correct answer:

S =  277.2 cm²

Step-by-step explanation:

$$\begin{gathered} a=5\text{cm} \\ u=8\text{cm} \\ h=12\text{cm} \\ q=100\%+5\%=1+\frac{5}{100}=1.05 \\ {S}_1=a\cdot h=5\cdot 12=60{\text{cm}}^2 \\ s=(a+a+u)/2=(5+5+8)/2=9\text{cm} \\ {S}_2=\sqrt{s\cdot (s-a)\cdot (s-a)\cdot (s-u)}=\sqrt{9\cdot (9-5)\cdot (9-5)\cdot (9-8)}=12\text{cm} \\ S=q\cdot (4\cdot S_1+2\cdot S_2)=1.05\cdot (4\cdot 60+2\cdot 12)=277.2{\text{cm}}^2 \end{gathered}$$

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