The Greeks had known how to find the areas of a triangle, rectangle, circle etc., and possibly, Archimedes invented these formulas. Recently, I read that given a parabola in a plane and a line intersecting the parabola at two points, Archimedes calculated the area of the region between line and parabola.
It will be a great pleasure for me if one shares such formulas of areas, of different nice shapes, which were invented by Greeks (or before them!) and also a reference for it.