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.

**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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