$\displaystyle a, b, c$ are the lengths of the sides of a triangle.

When they satisfy the equations : $\displaystyle a^2+b^2+c^2=6, a^4+b^4+c^4=14$, find the area of the triangle.

I got to finding the value of $\displaystyle a^2b^2+b^2c^2+c^2a^2$ , but I can't progress any further.