formula - volume of a tetrahedron????

Area of an equilateral triangle = (√3/4)a²

Area of the base: (√3/4)a²

Volume of a pyramid: (1/3) × Area of base × height

Height = ?

Note that the vertex at the top, one corner at the triangle at the base and the circumcentre form a right angled triangle.

The hypotenuse is 'a'
The base is a/√3
The height will be √(2/3)a

The volume will be
V = (1/3) × Area of base × height
= (1/3) × √3a²/4 × a√(2/3)
= a³/(6√2)

If a=8.6cm
V = 8.6³/(6√2) ≈ 74.96cm³

Vol of a tthn is (1/3) base(height).

Volume Of A Tetrahedron

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The formula for the volume of a tetrahedron is V = (√2/12)/a³, where a is the edge length. This can be derived from the more general formula for the volume of a cone, V = (1/3)Ah, having a base with area A and height h.

http://mathworld.wolfram.com/Tetrahedron.html