Elementary Geometry

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