A prismatoid is a polyhedron, possibly not convex, whose vertices all lie in one or the other of two parallel planes. The perpendicular distance between the two planes is called the altitude of the prismatoid. The faces that lie in the parallel planes are called the bases of the prismatoid. The midsection is the polygon formed by cutting the prismatoid by a plane parallel to the bases halfway between them.
The volume of a prismatoid is given by the prismoidal formula:
where is the altitude, and are the areas of the bases and is the area of the midsection.
An alternate formula is :
where is the area of the polygon that is formed by cutting the prismatoid by a plane parallel to the bases but 2/3 of the distance from to .
|Date of creation||2013-03-22 17:12:03|
|Last modified on||2013-03-22 17:12:03|
|Last modified by||Mathprof (13753)|