area

Area of polygon shape in geographic or planar coordinates

Since R2024a

Syntax

A = area(shape)

Description

A = area(shape) calculates the area of a polygon shape, which is the sum of the areas of the solid regions that comprise the shape.

Examples

Calculate Area of Polygon in Geographic Coordinates

Read world lakes into the workspace as a geospatial table. Extract the polygon shapes.

lakes = readgeotable("worldlakes.shp");
shape = lakes.Shape

shape=37×1 geopolyshape array with properties:
              NumRegions: [37×1 double]
                NumHoles: [37×1 double]
                Geometry: "polygon"
    CoordinateSystemType: "geographic"
           GeographicCRS: [1×1 geocrs]
      ⋮

Calculate the areas of the polygon shapes.

A = area(shape);

The units depend on the geographic coordinate reference system (CRS) for the shape. Find the length unit for the geographic CRS. The result indicates that the areas are in square meters.

shape.GeographicCRS.Spheroid.LengthUnit

ans = 
'meter'

Include the areas in the geospatial table by creating a new table variable. Sort the rows of the table in descending order by Area. Then, view the first eight rows of the table by using the head function.

lakes.Area = A;
lakes = sortrows(lakes,"Area","descend");
head(lakes)

       Shape                      Name                      Area   
    ____________    _________________________________    __________

    geopolyshape    "Caspian Sea"                        3.9124e+11
    geopolyshape    "Lakes Superior, Michigan, Huron"    2.0459e+11
    geopolyshape    "Lake Victoria"                      7.0562e+10
    geopolyshape    "Aral Sea"                           6.3581e+10
    geopolyshape    "Lake Baikal"                        3.3211e+10
    geopolyshape    "Great Bear Lake"                    3.2114e+10
    geopolyshape    "Lake Tanganyika"                    3.0947e+10
    geopolyshape    "Lake Malawi"                        3.0596e+10

Calculate Area of Polygon in Planar Coordinates

Read hydrographic data for Concord, MA into the workspace as a geospatial table. Extract the polygon shapes.

hydro = readgeotable("concord_hydro_area.shp");
shape = hydro.Shape

shape=98×1 mappolyshape array with properties:
              NumRegions: [98×1 double]
                NumHoles: [98×1 double]
                Geometry: "polygon"
    CoordinateSystemType: "planar"
            ProjectedCRS: [1×1 projcrs]
      ⋮

Calculate the areas of the polygon shapes.

A = area(shape);

The units depend on the projected coordinate reference system (CRS) for the shape. Find the length unit for the projected CRS. The result indicates that the areas are in square meters.

shape.ProjectedCRS.LengthUnit

ans = 
"meter"

Create a new geospatial table from the shape objects and the areas. View the first eight rows of the table by using the head function.

hydro_area = table(shape,A,VariableNames=["Shape","Area"]);
head(hydro_area)

       Shape           Area   
    ____________    __________

    mappolyshape        2456.4
    mappolyshape    1.2685e+05
    mappolyshape        2075.4
    mappolyshape        814.05
    mappolyshape         10754
    mappolyshape        5894.2
    mappolyshape         48368
    mappolyshape         27673

Input Arguments

shape — Polygon shape

geopolyshape object | mappolyshape object | array of geopolyshape objects | array of mappolyshape objects

Polygon shape, specified as a geopolyshape object, a mappolyshape object, an array of geopolyshape objects, or an array of mappolyshape objects.

Output Arguments

A — Area

array

Area, returned as an array. The size of A matches the size of shape.

The units of A depend on the type of polygon shape.

• When shape contains geopolyshape objects, the length unit of the reference ellipsoid for the shape determines the units. To find the length unit, get the geocrs object for the shape by querying the GeographicCRS property of the shape object. Then, get the ellipsoid by querying the Spheroid property of the geocrs object. If the ellipsoid is a referenceEllipsoid or referenceSphere object, then query the LengthUnit property of the ellipsoid. For a shape shp, the length unit is shp.GeographicCRS.Spheroid.LengthUnit. If the GeographicCRS property of the object is empty, the function calculates the area using the WGS84 reference ellipsoid and a length unit of meters.

• When shape contains mappolyshape objects, the length unit of the projected coordinate reference system for the shape determines the units. To find the length unit, get the projcrs object for the shape by querying the ProjectedCRS property of the shape object. Then, query the LengthUnit property of the projcrs object. For a shape shp, the length unit is shp.ProjectedCRS.LengthUnit.

When shape contains geopolyshape objects, the area function calculates the areas using geodesics.

Data Types: double

Limitations

The area function does not support some large polygons that cover more than a hemisphere.

Tips

The accuracy of the area function depends on the resolution of the data used to create the polygons. As a result, the function can return different results when you use polygon shapes from different data sets as inputs. This image compares the areas of polygon shapes for the state of Florida from two data sets.

Version History

Introduced in R2024a