Original sentence: In geometry, for a finite planar surface of scalar area , the vector area.This can only be defined for flat surfaces, or for regions of curved surfaces which are sufficiently small that they can be considered flat.This is due to  local homeomorphism.pl:Wektor powierzchni
Edited sentence: As an extreme example, a closed surface can possess arbitrarily large area, but its vector area is necessarily zero.First, we split the surface into infinitesimal elements, each of which is effectively flat.For a curved or faceted surface, the vector area is smaller in magnitude than the area.For an orientable surface S composed of a set  of flat facet areas, the vector area of the surface is given by.For bounded, oriented curved surfaces that are sufficiently well-behaved, we can still define vector area.For each infinitesimal element of area, we have an area vector, also infinitesimal.Integrating gives the vector area for the surface.Surfaces that share a boundary may have very different areas, but they must have the same vector area---the vector area is entirely determined by the boundary.These are consequences of Stokes theorem.pl:Wektor powierzchniIn geometry, for a finite planar surface of scalar area , the vector area.where  is the local unit vector perpendicular to.where  is the unit normal vector to the area