# area: Area of a longitude/latitude polygon In geosphere: Spherical Trigonometry

## Description

Compute the area of a polygon in angular coordinates (longitude/latitude) on an ellipsoid.

## Usage

 ```1 2 3 4 5``` ```## S4 method for signature 'matrix' areaPolygon(x, a=6378137, f=1/298.257223563, ...) ## S4 method for signature 'SpatialPolygons' areaPolygon(x, a=6378137, f=1/298.257223563, ...) ```

## Arguments

 `x` longitude/latitude of the points forming a polygon; Must be a matrix or data.frame of 2 columns (first one is longitude, second is latitude) or a SpatialPolygons* object `a` major (equatorial) radius of the ellipsoid `f` ellipsoid flattening. The default value is for WGS84 `...` Additional arguments. None implemented

## Value

area in square meters

## Note

Use raster::area for polygons that have a planar (projected) coordinate reference system.

## Author(s)

This function calls GeographicLib code by C.F.F. Karney

## References

C.F.F. Karney, 2013. Algorithms for geodesics, J. Geodesy 87: 43-55. https://dx.doi.org/10.1007/s00190-012-0578-z. Addenda: http://geographiclib.sf.net/geod-addenda.html. Also see http://geographiclib.sourceforge.net/

` centroid, perimeter `
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```p <- rbind(c(-180,-20), c(-140,55), c(10, 0), c(-140,-60), c(-180,-20)) areaPolygon(p) # Be careful with very large polygons, as they may not be what they seem! # For example, if you wanted a polygon to compute the area equal to about 1/4 of the ellipsoid # this won't work: b <- matrix(c(-180, 0, 90, 90, 0, 0, -180, 0), ncol=2, byrow=TRUE) areaPolygon(b) # Becausee the shortest path between (-180,0) and (0,0) is # over one of the poles, not along the equator! # Inserting a point along the equator fixes that b <- matrix(c(-180, 0, 0, 0, -90,0, -180, 0), ncol=2, byrow=TRUE) areaPolygon(b) ```