# Regular Tetrahedron Formula

Pyramid on a triangular base is a tetrahedron. When a solid is bounded by four triangular faces then it is a tetrahedron. A right tetrahedron is so called when the base of a tetrahedron is an equilateral triangle and other triangular faces are isosceles triangles. When we encounter a tetrahedron that has all its four faces equilateral then it is regular tetrahedron.

Area of One Face of Regular Tetrahedron Formula:

\[\large A=\frac{1}{4}\sqrt{3}a^{2}\]

Total Surface Area of Regular Tetrahedron Formula:

\[\large A=a^{2}\sqrt{3}\]

Slant Height of a Regular Tetrahedron Formula:

\[\large a\left(\frac{\sqrt{3}}{2}\right)\]

Altitude of a Regular Tetrahedron Formula:

\[\large h=\frac{a\sqrt{6}}{3}\]

Volume of a Regular Tetrahedron Formula

\[\large V=\frac{a^{3}\sqrt{2}}{12}\]

### Solved Example

**Question:** What is the volume of a tetrahedron with sides 10 cm ?

**Solution:**

Here,

a = 10 cm

Using the formula of Volume of a Regular Tetrahedron:

$V=\frac{a^{3}\sqrt{2}}{12}$

$=\frac{10^{3}\sqrt{2}}{12}$

$=117.85\;cm^{3}$