Search on "User-created Visual Objects" in the Programming Help, opened by selecting Help:Programming. You can use the width and height (in axes units) properties: dx and dy
For example, to find the area of a triangle, whose name is polygon:
What about randomly shaped polygons? Shapes without formulas. Is there a known way to count pixels bound within the polygon? I am attempting to compare the areas of regions bound by a curve. The shapes of the areas can be outlined with the polygon tool, but I do not know how to calculate the area of the region inside the polygon.