A scribal area of triangles and other shapes area calculation method is reported by three Rhind Mathematical Papyrus problems RMP 53-55. The scribal geometry utilized quotients and remainders in an arithmetic context that was looked like scribal weights and measures, algebra, and/or 2/n tables calculations.
RMP 53 calculated the area of two triangles, of 45/8 setat and 63/8 setat, and a third area of an undefined shape by the note, 1/10 of 1 3/8 mh added to 10 cubits of land (COL) is the desired area. A setat was 100 cubit by 100 cubit, or 10,000 square cubits. A cubit of land (COL), or mh, was one cubit wide by 100 cubits long, or 1/100 setat.
The first triangle had an altitude of 5 khet and a base of 9/4 khet. Using the area of a triangle formula, 1/2 the base times the altitude, 5*(9/4)*(1/2)= (45/8) = 5 5/8 setat.
The second triangle had an altitude of 7 khet and a base of 9/4 khet. Using the area of a triangle formula, 1/2 the base times the altitude, Ahmes calculated 7*(9/4)*(1/2) = 63/8 = 7 7/8 setat
The third calculation found the area of undefined shape discussed by:
Scholars have suggested that a truncated pyramid or a triangle defined the third shape.
To assist the decoding of the third RMP 53 area RMP 54, and RMP 55 setat and mh data have been consulted.
RMP 54 partitioned 7/10 setat by 10, 5, 2 1/2 and 1 1/4 segments. Proof was provided by multiplying one setat by 7/10, 14/10, 28/10 and 56/10 within a quotient and remainder context. A quotient setat and a scaled remainder mh were scaled as the 2/n table and a ro unit in hekat (volume unit) were scaled, by writing: