Find the area of the parallelogram whose vertices are at and

Hello!

This figure is really a parallelogram, for example because the opposite sides
have the same length: and Or we can check that the opposite sides have the same slope.

The area of a parallelogram is twice the area of the triangle (or  or or ). Therefore it is

The simplest way to compute this for the points with known coordinates is to note that this expression is the absolute value of the cross product:

This is the answer. If you don't know the cross product, you can use Heron's formula for any mentioned triangle (and multiply by 2).