# Find the Area of the Parallelogram

1. Feb 13, 2012

### Lurid

1. The problem statement, all variables and given/known data
Find the area of the paralellogram with vertices P1, P2, P3, and P4. *Not all pairs of vertices will give rise to a side.

P1 = (1, 2, -1)
P2 = (4, 2, -3)
P3 = (6, -5, 2)
P4 = (9, -5, 0)

2. Relevant equations
||U X V || is the area of the parallelogram having U≠0 and V≠0 as adjacent sides.

3. The attempt at a solution

How do you know which set of points will create a vector that are adjacent to each other?

2. Feb 14, 2012

### HallsofIvy

Staff Emeritus
You are told that this is a parallelogram- opposite sides must be parallel to one another.

3. Feb 14, 2012

### LCKurtz

And usually such problems give the points going around the object. So if it is a parallelogram and the points aren't mixed up, you might expect $P_1P_2$ and $P_3P_4$to be opposite sides. Of course, you would have to check to see if those two sides are parallel to see if that is true...