View source for Regular tetrahedron/Introductory problem

==Problem==

Find the volume of a tetrahedron whose sides all have length <math>2</math>.

==Solution==
We find the [[area]] of the [[base]]:

<math>\mathrm {A} =\dfrac{4\sqrt{3}}{4}=\sqrt{3}</math>

Now we find the [[lateral height]]:

<math>\mathrm {lh}=\sqrt{2^2-1^2}=\sqrt{3}</math>

Now we can find the height of the tetrahedron:

<math>\mathrm {h}=\sqrt{\sqrt{3})^2-(\dfrac{1}{3}*\sqrt{3})^2}=\sqrt{\dfrac{8}{3}</math>

Now the volume of the tetrahedron is:

<math>\dfrac{1}{3}*\sqrt{3}*\sqrt{\dfrac{8}{3}}=\dfrac{\sqrt{8}}{3}</math>
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