Hexagon, hexa S, V

What is the surface area and volume of a regular hexagonal prism with a base edge of 12 cm and a height equal to the diameter of the circle circumscribed about the base?

Final Answer:

S =  2476.2459 cm²
V =  8978.9514 cm³

Step-by-step explanation:

$$\begin{gathered} a=12\text{cm} \\ D=2\cdot a=2\cdot 12=24\text{cm} \\ h=D=24\text{cm} \\ n=6 \\ {S}_1=\frac{\sqrt{3}}{4}\cdot a^2=\frac{\sqrt{3}}{4}\cdot 12^2=36\sqrt{3}{\text{cm}}^2\doteq 62.3538{\text{cm}}^2 \\ {S}_2=n\cdot S_1=6\cdot 62.3538=216\sqrt{3}{\text{cm}}^2\doteq 374.123{\text{cm}}^2 \\ o=n\cdot a=6\cdot 12=72\text{cm} \\ S=2\cdot S_2+o\cdot h=2\cdot 374.123+72\cdot 24=2476.2459{\text{cm}}^2 \end{gathered}$$

$V=S_2\cdot h=374.123\cdot 24=8978.9514{\text{cm}}^3$

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