They used the 20 finger remen.
They used the 28 finger cubit.
They used the diagonal of a remen for doubling area.
Hence the length of the diagonal of a remen square is 28.28427 fingers.

The result is two possible cubit lengths. A 28 finger cubit and a cubit a little longer.
The ratio between those two cubits is
28 / (20 x square root 2) = 0.98995

This is exactly the same as the ratio from the base to the apex and from the first course to the apex. Hence does the;
1st course to apex = 280 cubits of 28 fingers
Base to apex = 280 cubits of remen square diagonal (20 fingers x square root 2)

The result is the actual height becomes;
280 / 0.9899 = 282.8427 cubits of 28 fingers
282.8427 is the square root of 80,000 or 8 x 100 x 100.

This bring us to the comments of Herodotus stated earlier thanks to Lee's source.

......................

têi de puramidi autêi chronon genesthai eikosi etea poieumenêi: tês esti pantachêi [every side] metôpon [face] hekaston [each one] oktô [eight]. plethra [100 feet or 100x100 feet] eousês [to be/exist] tetragônou [square] kai [and] hupsos [height] ison [equal], lithou de xestou te kai harmosmenou ta malista: oudeis tôn lithôn triêkonta podôn elassôn.

"......every side face, each one 8 plethra (to be square) and height equal."


kai = and
pantechei on every side
metopon - front face of anything, as of a wall or building
okto – eight
plethron – a measure of length of 100’ [or a measure of area 100' x 100']
eouses – to be / exist
hekaston – each one
hupsos - height
ison - equal
tetragonou - square as in tetragon