The shoelace formula, also known as Gauss's area formula, the shoelace algorithm, shoelace method, or surveyor's formula, is a name sometimes given to the polygon area formula for the area of a simple polygon in terms of the Cartesian coordinates of its vertices , ..., .
The area of such a polygon is
(1)
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where denotes a determinant. When recast in abbreviated form (which is actually an abuse of determinant notation) as
(2)
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(3)
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the result is sometimes known as the shoelace formula due to the placement of terms with alternating signs resembling the alternating crossings of laces on the front of a show.