Editing Prismatoid (section)

==Volume==
If the areas of the two parallel faces are {{math|''A''{{sub|1}}}} and {{math|''A''{{sub|3}}}}, the cross-sectional area of the intersection of the prismatoid with a plane midway between the two parallel faces is {{math|''A''{{sub|2}}}}, and the height (the distance between the two parallel faces) is {{mvar|h}}, then the [[volume]] of the prismatoid is given by{{r|meserve}}
<math display="block">V = \frac{h(A_1 + 4A_2 + A_3)}{6}.</math>
This formula follows immediately by [[integral|integrating]] the area parallel to the two planes of vertices by [[Simpson's rule]], since that rule is exact for integration of [[polynomial]]s of degree up to 3, and in this case the area is at most a [[quadratic function]] in the height.