# Equal-Area Parallelograms Using Determinants

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All three of the parallelograms on the left have the same area.

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To find the area of the green parallelogram defined by the points , , and , take the absolute value of the determinant of a matrix. The inputs for the rows in the green matrix are and .

However, you can also find the area of the same parallelogram by taking the absolute value of the determinant of a matrix with the row inputs and (red) and a matrix with the row inputs and (blue). The absolute value of all three of these determinants is the same.

So, in order to find the area of the original green matrix using determinants, the inputs for the rows of the matrix can be any two of the three points (, and ).

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Contributed by: Talia Shaw (June 2021)
Suggested by: Matthew Hoek
Open content licensed under CC BY-NC-SA

## Details

Snapshot 1: parallelogram defined by the points , , and

Snapshot 2: parallelogram defined by the points , , and

Snapshot 3: parallelogram defined by the points , , and

## Permanent Citation

Talia Shaw

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