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)