Formulas

Elementary Geometry

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