# Cuboid

Cuboid has a surface of 516 cm2. Side a = 6 cm and b = 12 cm. How long is the side c =?

Result

c =  10.333 cm

#### Solution:

$a = 6 \ cm \ \\ b = 12 \ cm \ \\ S = 516 \ cm^2 \ \\ S = 2(ab+bc+ac) \ \\ c = (S/2 - a \cdot \ b)/(b+a) = (516/2 - 6 \cdot \ 12)/(12+6) = \dfrac{ 31 }{ 3 } \doteq 10.3333= 10.333 \ \text { cm } \ \\ S_{ 2 } = 2 \cdot \ (a \cdot \ b+b \cdot \ c+a \cdot \ c) = 2 \cdot \ (6 \cdot \ 12+12 \cdot \ 10.3333+6 \cdot \ 10.3333) = 516$

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