[Math] Find the area of the parallelogram with vertices (4,1), (6, 6), (7, 7), and (9, 12).

Question

I am trying to find the area of the parallelogram with vertices (4,1), (6, 6), (7, 7), and (9, 12).

So I believe the way to solve this problem is through the cross product and then taking the magnitude. However, I got the wrong answer and I am now rethinking my methods.

My original work:

Point A:(4,1)
Point B: (6,6)
Point C:(7,7)
Point D: (9,12)

I took the cross product of AB and AC and took the magnitude of that and ended up getting sqrt(369).

I would appreciate the help. I am kind of stumped.

Answer 1

See this illustration on how to compute the area of a parallelogram in an easy manner.