Determinant for of Area of triangle in 3D

Question

As we all know that area of a triangle is given by absolute value of the determinant of this matrix$ A = \dfrac 1 2 {\left| \begin{vmatrix} x_1 & y_1 & 1 \\ x_2 & y_2 & 1 \\ x_3 & y_3 & 1 \\ \end{vmatrix} \right|}, $ for 2D coordinates system. However is there a formula involving determinants for 3D Coordinates.
(Note: I know that we can use cross products of vectors to find area of triangle for 3D coordinates and that it works for general n coordinates but I wanted to know if there exists a formula for 3D in determinant form(even if its probably impractical to use it))