# Regular tetrahedron/Introductory problem

## Problem

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

## Solution

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. ! Missing } inserted.)

Now the volume of the tetrahedron is: