Using Determinant to find the Area of a Parallelogram

Related Pages
Determinant of a 2×2 Matrix
Inverse of a 2×2 Matrix
Matrices
[More Lessons for Grade 9

Area Determinant
One thing that determinants are useful for is in calculating the area determinant of a parallelogram formed by 2 two-dimensional vectors.
The matrix made from these two vectors has a determinant equal to the area of the parallelogram.
Area determinants are quick and easy to solve if you know how to solve a 2×2 determinant.
A parallelogram in three dimensions is found using the cross product.

Linear Algebra Example Problems - Area Of A Parallelogram
Also verify that the determinant approach to computing area yield the same answer obtained using “conventional” area computations.

Example:
Consider the parallelogram with vertices (0,0) (7,2) (5,9) (12,11)
Sketch and compute the area.

How to compute the area of a parallelogram using a determinant?

Determinant and area of a parallelogram
Realizing that the determinant of a 2x2 matrix is equal to the area of the parallelogram defined by the column vectors of the matrix.

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