Pyramid height

Find the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height h = 20cm.

Correct answer:

V =  415.6922 cm³

Step-by-step explanation:

$$\begin{gathered} a=12\text{ cm } \\ h=20\text{ cm } \\ {S}_1={\displaystyle \frac{\sqrt{3}}{4}}\cdot a^2={\displaystyle \frac{\sqrt{3}}{4}}\cdot 12^2=36\sqrt{3}{\text{cm}}^2\doteq 62.3538{\text{cm}}^2 \\ V={\displaystyle \frac{1}{3}}\cdot S_1\cdot h={\displaystyle \frac{1}{3}}\cdot 62.3538\cdot 20=240\sqrt{3}=415.6922{\text{cm}}^3 \end{gathered}$$

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