= \frac{1}{6}\sqrt{\, \begin{vmatrix} a^2 & \frac{a^2+b^2-ab^2}{2} & \frac{a^2+c^2-ac^2}{2} \\ \frac{a^2+b^2-ab^2}{2} & b^2 & \frac{a^2+c^2-ac^2}{2} \\ \frac{a^2+c^2-ac^2}{2} & \frac{a^2+c^2-ac^2}{2} & c^2 \end{vmatrix}}