Read the result
The parallelogram area is |A x B|. A triangle using the same two sides is exactly half of that.
Vector algebra
Area From Cross Product
Use the cross product magnitude to get parallelogram and triangle area from side vectors.
Formula
Area(parallelogram) = |A x B|, Area(triangle) = |A x B| / 2
Result
Worked substitution
The magnitude of the cross product measures the area swept out by the two vectors.
Where it helps
This is faster than coordinate geometry when a 3D triangle or sloping parallelogram is described by vectors.
Common slip
Only halve the area for a triangle. The cross product magnitude itself is the parallelogram area.
Try it
Make the two vectors parallel. The area should collapse to 0.