Let , and be the vertices of the triangular region as shown in the given diagram. Draw perpendiculars from the points , and on the X-axis at the points , and respectively. There are three trapezoidal regions formed in this way.
The area of the triangular region = the area of trapezoidal region + the area of trapezoidal region - the area of trapezoidal region
This formula can be written in the determinant form as follows:
This gives the area of the triangular region. The negative sign should be omitted if it occurs, as the area should be positive.
NOTE: If the three points , and are collinear points (lying on the same line), then no triangular region will form and the area will be zero, so the condition for three points , and to be collinear is that