The prismatoid theorem states that the volume of a prismatoid is equal to the sum of the volumes
of a pyramid, a wedge, and
a parallelepiped. For proof and details of the
decomposition, see Kern and Bland (1948, pp. 121-130).
The name "prismatoid theorem" is also used for the volume
formula
Kern, W. F. and Bland, J. R. "Prismatoid Theorem," "Proof of the Prismoidal Formula," and "Application
of Prismatoid Theorem." §43-45 in Solid
Mensuration with Proofs, 2nd ed. New York: Wiley, pp. 121-130, 1948.
is the altitude of the prismatoid,
and 
are the areas of its two bases,
and 
is the area of the cross section
halfway between and parallel to the bases.
