Areas from Vectors

compass
 
Move the blue points below to change the vectors that define the parallelogram.
As you move the vectors, notice how the area changes.
 

 

Can you find a formula for the area of a parallelogram if you know the two vectors?

Can you explain why your formula works?

What is the formula in the special case when the parallelogram is a square?

What is special about the areas of the rhombuses you can make?