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