Surveying & Geomatics

Intermediate

Area by Coordinates (Shoelace)

Area of a polygon from the coordinates of its corners.

Formula

A = \frac{1}{2}\left| \sum (x_i y_{i+1} - x_{i+1} y_i) \right|

Variables

AArea

x_i, y_iVertex coordinates

Example

Triangle (0,0),(4,0),(0,3): A = ½|12| = 6

Did You Know?

The name comes from the crisscross multiplication pattern that looks like lacing a shoe.

surveying area polygon

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