PYTHAGOREAN THEOREM PROBLEM
of the GREAT PYRAMID

South triangle's area = 0.61938
East triangle's area = 0.619744

Since for a triangle:
area= base * altitude / 2
solving for altitude gives:
South triangle's altitude = 0.786424
East triangle's altitude = 0.787096

But

PROBLEM: The triangle's altitude does not match the altitude given by the apothem's right triangle.
The actual altitude is different:
South =.782375 East = .782933