Definition:Area Element

Definition
An area element $\delta S$ is a (usually) infinitesimal area of a plane, often the surface of a bodyin space, (usually) containing a particular point $P$.

In the cartesian $3$-space such an area element is modelled as a rectangle whose edges are parallel to two of the coordinate axes, and assigned lengths $\delta x$, $\delta y$ or $\delta z$ respectively.