# Parallelogram area using determinant

Given a Parallelogram with the co-ordinates: $(a+c, b+d), (c,d), (a, b)$ and $(0, 0)$

I have to prove that the area of the Parallelogram is: $|ad-bc|$ as in the determinant of:

$$\begin{bmatrix} a & b\\ c & d \end{bmatrix}$$

How do I even begin using the concept of determinants for this geometrical question?

Firstly, show that the transformation of the points of the unit square map to the parallelogram that you show. Secondly, calculate the area of a parallelogram using some basic symmetries of the shape and show it is $|a d - b c|$. This is in fact the basic principle behind determinants, they were invented to see how the area of shapes change under a matrix transformation.
How you show the area depends on what you already know. If you know about complex numbers, think about what the imaginary part of $\bar{z_1} z_2$ represents.