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
Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.