When I was driving home from work today I noticed a for sale sign for a plot of land that said “+ or – 2.9 Acres.” It had me wondering how they came to that number. Im sure lots of plots of land for sale are sold in squares, but I live in a very old state so property lines must be all over the place.
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One method is to use the [surveyor’s formula](https://en.wikipedia.org/wiki/Shoelace_formula). This requires representing the plot boundary as a polygon (shape made of straight lines) and knowing the coordinates of the vertices (corners).
This formula doesn’t take the curvature of the earth into account so it would become less accurate for larger shapes. The simplest way around this is to first convert the coordinates to an equal-area map projection.
Another issue is that some surveying boundaries contain circular arcs instead of straight lines. One way to deal with this is to first replace each arc with a straight line joining its end-points and then use the surveyor’s formula. Afterwards you can add or subtract the area between the line and the arc which can be calculated using a different formula.
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