Hexagonal pyramid

Find the volume of a regular hexagonal pyramid, the base edge of which is 12 cm long and the side edge 20 cm.

Correct answer:

V =  1995.3225 cm³

Step-by-step explanation:

$$\begin{gathered} a=12\text{ cm } \\ s=20\text{ cm } \\ {S}_0=\sqrt{3}\mathrm{/}4\cdot a^2=\sqrt{3}\mathrm{/}4\cdot 12^2=36\sqrt{3}{\text{cm}}^2\doteq 62.3538{\text{cm}}^2 \\ {S}_1=6\cdot S_0=6\cdot 62.3538=216\sqrt{3}{\text{cm}}^2\doteq 374.123{\text{cm}}^2 \\ {s}^2=h^2+a^2 \\ h=\sqrt{s^2-a^2}=\sqrt{20^2-12^2}=16\text{ cm } \\ V={\displaystyle \frac{1}{3}}\cdot S_1\cdot h={\displaystyle \frac{1}{3}}\cdot 374.123\cdot 16=1995.3225{\text{cm}}^3 \end{gathered}$$

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