Common Core (Vector and Matrix Quantities)
Common Core for Mathematics
Examples, solutions, videos, and lessons to help High School students learn to work with 2 × 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area.
Common Core: HSN-VM.C.12
The following diagram shows how to use determinants to find the area of a polygon. Scroll down the page for more examples and solutions.
2D Area and determinants
Introduction to calculating area of a parallelogram in the plane using a 2×2 determinant.
Area of a triangle with determinants
This method uses the formula of the parallelogram, by moving the triangle such that one vertex is at the origin.
Determinants to Find the Area of a Triangle
This video shows how to use determinants to find the area of a triangle where the vertices are not at the origin.
Determinants to Find the Area of a Polygon
This video shows how one can use determinants to find the area enclosed by any polygon.
Application of Determinants: Area on the Coordinate Plane
This video shows how to use determinants to calculate the area of a triangle and parallelogram on the coordinate plane.
The formula involves finding the determinant of a 3x3 matrix.
Determinant of a matrix as the area scale factor of the transformation
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