How do you find the area of a parallelogram with four given vertices?

Question

Find the area of the parallelogram with vertices at (3, -3), (13, -5), (4, -15), and (14, -17).

Answer 1

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.

|x₁ y₁ 1|

|x₂ y₂ 1|

|x₃ y₃ 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.