Box

Cardboard box shaped quadrangular prism with a rhombic base. Rhombus has a side 5 cm and one diagonal 8 cm long and height of the box is 12 cm. The box will open at the top.

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

Result

S =  277.2 cm²

Solution:

$S_1 = 5 \cdot 12 = 60 \ cm^2 \ \\ s = (5+ 5 + 8 )/2 = 9 \ \\ S_2 = \sqrt{ s(s-5)(s-5)(s-8)} \ \\ S_2 = \sqrt{ 9(9-5)(9-5)(9-8)} = 12 \ \\ \ \\ S = (1+5/100) (4 \cdot S_1 + 2 \cdot S_2) \ \\ S = 1.05 \cdot (240 + 24) = 277.2 \ cm^2$

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