Approximately 2300 years ago Eudoxus, Archimedes and others encouraged the area of the circle through the exhaustion method, which consists of circumscribing and inscribing regular polygons in the figure that is intended to evaluate the area. Area of the circle - Greek Method Initially, let’s define the area of a square region. Definition: The area of a square region of side $a$ is $a^2$. The Greeks verified that every polygonal region can be inscribed in a square through a finite number of operations with a ruler and compass.