Similarly, one might guess that the pyramidal numbers are proportional to the triangular numbers and divide a pyramidal number by its corresponding triangular number. One again gets a linear sequence of numbers and the factor can be easily determined.
So it is not always obvious how a particular formula was arrived at. The formulas found in the ancient papyri were probably intended for use by scribes functioning as clerks and probably do not comprise a mathematical treatise. The ultimate source of the procedures may have been lost with the passage of time and what we now have may have been copied and recopied over thousands of years.
The procedures given in the mathematical papyri are in the most general form. One finds both the method for finding the area of a truncated triangle (with the upper portion cut off parallel to the bottom) and the volume of a truncated pyramid.
For more information see,
The Rhind Mathematical Papyrus by Gay Robins and Charles Shute
Mathematics and Measurement by O. A. W. Dilke
Mathematics in the Time of the Pharaohs by Richard J. Gillings