Measuring land tax in old Egypt

As a student, I was once tasked with giving a talk in my English class. I came up with a simple demonstration of the quadruature of a polygon using only a piece of rope and sticks. I imagined that such a construction might have been used by an engineer in ancient Egypt who was tasked by the Pharaoh with calculating the land tax for a field. I assumed that the engineer did not perform any math himself, and that a priest—someone who could square numbers himself or could employ a deity to do it for him—provided him with a table in the form tax/side-length for square fields. I might have even read somewhere that such tables existed and sometimes contained errors.

Note: I should think about something similar in 3D (Hilbert’s third problem).