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Area from coordinates

The area of a plot with known corner coordinates can be calculated directly with the coordinate method. You go round the polygon and sum cross products. The method works for any polygon that does not cross itself.

A=12∣∑i(xi yi+1−xi+1 yi)∣A = \tfrac12\left|\sum_{i} (x_i\,y_{i+1} - x_{i+1}\,y_i)\right|coordinate method (shoelace formula)

Symbols

xi, yix_i,\ y_icoordinates of corner im
AAaream²

Example

Rectangle (0,0), (20,0), (20,10), (0,10):

12∣0+200+200+0∣=200\tfrac12|0 + 200 + 200 + 0| = 200 m².

The corners must be taken in order around the plot, or the answer is wrong.
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← Coordinates and distance

Part of Building and Structures: Surveying.