This figure shows a cube decomposed along the diagonal into
3 square pyramids
(the bottom square of the cube is the base of one pyramid, the square
face towards us is another base, and the square face on the right side is
which would explain why the
volume of a square pyramid is one-third the height times the base.
Are they congruent pyramids though?
To answer this question you may wish to play with
Geoblocks (you can sign a kit out from the math/science education
center on the second floor) or build models
from nets or other sources.