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Surface area of latitude-longitude quadrangle

`area = areaquad(lat1,lon1,lat2,lon2)area = areaquad(lat1,lon1,lat2,lon2,ellipsoid)area = areaquad(lat1,lon1,lat2,lon2,ellipsoid,`

`area = areaquad(lat1,lon1,lat2,lon2)` returns
the surface area bounded by the parallels `lat1` and `lat2` and
the meridians `lon1` and `lon2`.
The output `area` is a fraction of the unit sphere's
area of 4π, so the result ranges from 0 to 1.

`area = areaquad(lat1,lon1,lat2,lon2,ellipsoid)` allows
the specification of the ellipsoid model with `ellipsoid`. `ellipsoid` is
a `referenceSphere`, `referenceEllipsoid`, or `oblateSpheroid` object, or a vector
of the form `[semimajor_axis eccentricity]`. When `ellipsoid` is
input, the resulting `area` is given in terms of
the (squared) units of the ellipsoid. For example, if the ellipsoid `referenceEllipsoid('grs80','kilometers')` is
used, the resulting area is in km^{2}.

`area = areaquad(lat1,lon1,lat2,lon2,ellipsoid,units)` specifies
the units of the inputs. The default is

A latitude-longitude quadrangle is a region bounded by two meridians
and two parallels. In spherical geometry, it is the intersection of
a *lune* (a section bounded by two meridians) and
a *zone* (a section bounded by two parallels).

Find the fraction of the Earth's surface that lies between 30ºN and 45ºN, and also between 25ºW and 60ºE:

area = areaquad(30,-25,45,60) area = 0.0245

Assuming a spherical ellipsoid, find the surface area of the Earth in square kilometers.

earthellipsoid = referenceSphere('earth','km'); area = areaquad(-90,-180,90,180,earthellipsoid) area = 5.1006e+08

For comparison,

earthellipsoid.SurfaceArea ans = 5.1006e+08

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