In a 2D plane,
For three points
A (x _{ 1 } , y _{ 1 } ),
B (x _{ 2 } , y _{ 2 } ),
C (x _{ 3 } , y _{ 3 } )
Find area of triangle with vertices (3, 8), (4, 2), (5, 1)
Check solution  Example 17
For points in 3D plane
A (x _{ 1 } , y _{ 1 } , z _{ 1 } )
B (x _{ 2 } , y _{ 2 } , z _{ 2 } )
C (x _{ 3 } , y _{ 3 } , z _{ 3 } )
There are some points to note:

If Area of triangle = 0,
then the three points are collinear

If value of determinant comes negative, we will take the
positive value as area
Example
Therefore,
Area = 45 square units

.If area is given,
We take both positive and negative value of determinant
Example
If Area = 3 square units
Check the questions below to learn more