Hexagonal prism

The base of the prism is a regular hexagon consisting of six triangles with side a = 12 cm and height va = 10.4 cm. The prism height is 5 cm. Find the volume and surface of the prism.

Correct result:

V =  1870.6149 cm³
S =  1108.2459 cm²

Solution:

$$\begin{gathered} a=12\text{ cm } \\ h=5\text{ cm } \\ o=6\cdot a=6\cdot 12=72\text{ cm } \\ v=\sqrt{a^2-(a\mathrm{/}2{)}^2}=\sqrt{12^2-(12\mathrm{/}2{)}^2}=6\sqrt{3}\text{ cm}\doteq 10.3923\text{ cm } \\ {S}_1=a\cdot v\mathrm{/}2=12\cdot 10.3923\mathrm{/}2=36\sqrt{3}{\text{cm}}^2\doteq 62.3538{\text{cm}}^2 \\ {S}_6=6\cdot S_1=6\cdot 62.3538=216\sqrt{3}{\text{cm}}^2\doteq 374.123{\text{cm}}^2 \\ V=S_6\cdot h=374.123\cdot 5=1870.6149{\text{cm}}^3 \end{gathered}$$

$S=2\cdot S_6+o\cdot h=2\cdot 374.123+72\cdot 5=1108.2459{\text{cm}}^2$

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