Applications of Determinants, Area of the Triangle

Applications of Determinants, Area of the Triangle

Areas:

Triangle:

Consider the triangle with vertices 

 and .

Formula for the area of the triangle is

.

Example 2:

Compute the area of the triangle with vertices  and .

Solution:

The area is

.

Parallelogram:

Suppose we have a parallelogram with vertices 

,  and ,

Then, the area of the parallelogram is