Regular tetrahedron/Introductory problem

Problem

Find the volume of a tetrahedron whose sides all have length .

Solution

We find the area of the base:

Now we find the lateral height:

Now we can find the height of the tetrahedron:

$\mathrm {h}=\sqrt{\sqrt{3})^2-(\dfrac{1}{3}*\sqrt{3})^2}=\sqrt{\dfrac{8}{3}$ (Error compiling LaTeX. Unknown error_msg)

Now the volume of the tetrahedron is:

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