# Formulas and Tables

Elementary Geometry# Tetrahedron

Edge of a regular tetrahedron: \(a\)

Height of a tetrahedron: \(h\)

Volume: \(V\)

Area of the base: \({S_B}\)

Surface area: \(S\)

- In a regular tetrahedron, all four faces are equilateral triangles.
- Relationship between the edge length and the height in a regular tetrahedron

\(h = a\sqrt {\large\frac{2}{3}\normalsize} \) - Area of the base of a regular tetrahedron

\({S_B} = {\large\frac{{{a^2}\sqrt 3 }}{4}\normalsize}\) - Total surface area of a regular tetrahedron

\(S = {a^2}\sqrt 3 \) - Volume of a regular tetrahedron

\(V = {\large\frac{1}{3}\normalsize}{S_B}h = {\large\frac{{{a^2}}}{{6\sqrt 2 }}\normalsize}\)