If the co-ordinates of the vertices of an equilateral triangle with sides of length ‘a’ are (x₁,y₁), (x₂,y₂), (x₃,y₃) then
| x₁ y₁ 1 |²
| x₂ y₂ 1 | = 3a⁴/4
| x₃ y₃ 1 |