# Area of a triangle in 4-space

1. Mar 21, 2012

1. The problem statement, all variables and given/known data
Find the area of triangle with vertices (-2,-2,2,2), (0,0,1,-1), (-1,-2,1,1)

2. Relevant equations
3. The attempt at a solution
The only way I know how to find the area of a triangle is by finding half the parallelogram. I.e. A = (1/2)||u x v||

But this requires cross product and you can't find the cross product in 4-space, can you?

Any help/explaination would be greatly appreciated.

2. Mar 21, 2012

### Staff: Mentor

You'll need to form displacement vectors between pairs of vertices. You can then find the magnitudes of those displacement vectors. After that you can use the dot product to find the cosine of the angle between two adjacent sides of the triangle.

All three points lie in a plane (it happens to be in R4 but that's not important), so I would advise drawing a rough sketch of the three points. With a bit of trig you should be able to get the area of the triangle.

3. Mar 23, 2012