# prismatoid

The volume of a prismatoid is given by the prismoidal formula:

 $V=\frac{1}{6}h(B_{1}+B_{2}+4M)$

where $h$ is the altitude, $B_{1}$ and $B_{2}$ are the areas of the bases and $M$ is the area of the midsection.

An alternate formula is :

 $V=\frac{1}{4}h(B_{1}+3S)$

where $S$ 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 $B_{1}$ to $B_{2}$.

A proof of the prismoidal formula for the case where the prismatoid is convex is in . It is also proved in  for any prismatoid. The alternate formula is proved in .

Some authors impose the condition that the lateral faces must be triangles or trapezoids  . However, this condition is unnecessary since it is easily shown to hold.

## References

 Title prismatoid Canonical name Prismatoid Date of creation 2013-03-22 17:12:03 Last modified on 2013-03-22 17:12:03 Owner Mathprof (13753) Last modified by Mathprof (13753) Numerical id 10 Author Mathprof (13753) Entry type Definition Classification msc 51-00 Related topic SimpsonsRule Related topic Volume2 Related topic TruncatedCone Defines altitude Defines bases Defines prismoidal formula