Box

Cardboard box-shaped quadrangular prism with a rhombic base. Rhombus has a side 5 cm, and one diagonal 8 cm long, and the box's height is 12 cm. The box 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:

$$\begin{gathered} S_1=5\cdot 12=60c{m}^2 \\ s=(5+5+8)\mathrm{/}2=9 \\ {S}_2=\sqrt{s(s-5)(s-5)(s-8)} \\ {S}_2=\sqrt{9(9-5)(9-5)(9-8)}=12 \\ S=(1+5\mathrm{/}100)(4\cdot S_1+2\cdot S_2) \\ S=1.05\cdot (240+24)=277.2{\text{cm}}^2 \end{gathered}$$

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