Area with a determinant
Compute the area of parallelograms and triangles from vectors and coordinates with the two-row determinant.
- Germany: grade 8
- Syria: grade 10
- Palestine: grade 11
Guide
The determinant of two vectors a = (a₁|a₂) and b = (b₁|b₂) is det(a, b) = a₁ · b₂ – a₂ · b₁. Its absolute value is the area of the parallelogram spanned by a and b.
A triangle ABC has the area ½ · |det(AB, AC)|. The sign of the determinant tells the orientation; det = 0 means that the three points lie on a line.
This topic is part of the Realschule syllabus (Mathematik II/III).