There is a determinant which directly gives the area of a triangle given the co-ordinates of the vertices.

Divide the parallelogram into 2 triangles and use the determinant to get the area of each and add.

|x_{1} y_{1} 1|

|x_{2} y_{2} 1|

|x_{3} y_{3} 1|

I have written the determinant above as well as I can using this editor. The area of the triangle is 1/2 * the value of the determinant.

If you don't know how to do that, calculate the lengths of each of the 2 sides and a diagonal and use Heron's formula.