# Hexagon

Calculate the surface of a regular hexagonal prism whose base edge a = 12cm and side edge b = 3 dm.

Result

S =  2908.246 cm2

#### Solution:

$a = 12 \ cm \ \\ b = 3 \ dm = 3 \cdot \ 10 \ cm = 30 \ cm \ \\ \ \\ S_{ 0 } = \sqrt{ 3 }/4 \cdot \ a^2 = \sqrt{ 3 }/4 \cdot \ 12^2 = 36 \ \sqrt{ 3 } \ cm^2 \doteq 62.3538 \ cm^2 \ \\ S_{ 1 } = 6 \cdot \ S_{ 0 } = 6 \cdot \ 62.3538 = 216 \ \sqrt{ 3 } \ cm^2 \doteq 374.123 \ cm^2 \ \\ \ \\ S = 6 \cdot \ a \cdot \ b + 2 \cdot \ S_{ 1 } = 6 \cdot \ 12 \cdot \ 30 + 2 \cdot \ 374.123 \doteq 2908.2459 = 2908.246 \ cm^2$

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