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A triangular pyramid is a pyramid having a triangular base. The tetrahedron is a triangular pyramid having congruent equilateral triangles for each of its faces.
The edge length and slant height of a regular triangular pyramid is a special case of the formula for a regular -gonal pyramid with , given by
(1)
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(2)
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where is the height and is the length of a side of the base.
Like all pyramids, the volume of triangular pyramid is given by
(3)
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where is the area of the triangular base and is the height of the pyramid.
The regular tetrahedron is a special case of the triangular pyramid.