A tetrahedron is a three-dimensional shape with four triangular faces, three of which meet at a point called

**vertex**. Tetrahedron has 6 edges and 4 vertices. Tetrahedron is a type of pyramid.

Volume of a tetrahedron is same as that of volume of pyramid which is given as follows:

A

**regular tetrahedron** is a tetrahedron in which all four triangles are equilateral triangles. Following is the image showing a regular tetrahedron:

Let us assume that each side of regular tetrahedron is

**"a"**. Then,

Area of base = Area of equilateral triangle ΔBDC

Area of base =

$\frac{\sqrt{3}}{4}a^{2}$.........

**1**In right triangle BED, using Pythagorean theorem,

DE

^{2} = BD

^{2} - BE

^{2}DE =

$\sqrt{a^{2}-\frac{a^{2}}{4}}$DE =

$\frac{\sqrt{3}}{2}a$Since DE is a median of ΔBDC,

∴ DO =

$\frac{2}{3}$ DE

DO =

$\frac{2}{3}$ $\times$

$\frac{\sqrt{3}}{2}a$DO =

$\frac{\sqrt{3}}{3}a$In right triangle AOD, using Pythagorean theorem,

AO

^{2} = AD

^{2} - DO

^{2}AO =

$\frac{\sqrt{6}}{3}a$AO = height =

$\frac{\sqrt{6}}{3}a$ .........

**2**Using equation

**1** and

**2**, we obtain

Volume of regular tetrahedron =

$\frac{1}{3}$ $\times$

$\frac{\sqrt{3}}{4}a^{2}$$\times$

$\frac{\sqrt{6}}{3}a$Therefore, the formula for volume of regular tetrahedron is given below:

^{}