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: \(S\)

  1. A tetrahedron is a polyhedron composed of \(4\) triangular faces. The tetrahedron is a triangular pyramid.
Tetrahedron
  1. In a regular tetrahedron, all four faces are equilateral triangles.
  2. Relationship between the edge length and the height in a regular tetrahedron
    \(h = a\sqrt {\large\frac{2}{3}\normalsize} \)
  3. Area of the base of a regular tetrahedron
    \({S_B} = {\large\frac{{{a^2}\sqrt 3 }}{4}\normalsize}\)
  4. Total surface area of a regular tetrahedron
    \(S = {a^2}\sqrt 3 \)
  5. Volume of a regular tetrahedron
    \(V = {\large\frac{1}{3}\normalsize}{S_B}h = {\large\frac{{{a^2}}}{{6\sqrt 2 }}\normalsize}\)