Using Determinant to find the Area of a Parallelogram

These lessons, with videos, examples and step-by-step solutions, help Algebra students learn how to use the determinant to find the area of a parallelogram.

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Related Pages
Determinant of a 2×2 Matrix
Inverse of a 2×2 Matrix
[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.

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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