# Calculating the Area of a Country Using Green's Theorem

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Green's theorem shows the relationship between the length of a closed path and the area it encloses.

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Contributed by: Erik Mahieu (May 2013)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Snapshot 1: Shows the total area being independent of the position of the locator.

Snapshot 2: Shows the mostly positive areas (determinants) if the locator is in the middle. The direction of *Mathematica*'s CountryData coordinates is clockwise.

Snapshot 3: This illustrates the red positive areas and the blue negative ones. An intermediate color is generated when they overlap.

## Permanent Citation