In surveying, one checks whether the angles and distances form a closed polygon, and by how much it is off. If the area is sufficiently large, the polygon will not close no matter how accurately measured if it is calculated on a plane. The area of a polygon whose angle excess is 1 second of arc, which is the precision (though not necessarily the accuracy) of surveying, is 393 square kilometers, or about 20 kilometers square.
Angle deficit is defined similarly on a pseudosphere, and is likewise proportional to area in hyperbolic geometry.
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