Is it possible to calculate area of polygons from GPS points without POSTGIS

I am new with GIS.

Assume we use the UTM30N coordinate system.

Is it possible to calculate an area (say a square box) by the 4 given points? (assume the points are in order, and the coordinates are very close to each other.)

Corollary, is it possible to calculate the area of a polygon?

Can this be done without the use of PostGIS?