## The Prismatoid and the Prismoidal Formula

## The General Prismatoid

A * general prismatoid* is a solid such that the area of any section, say

*A*, parallel to and distant

_{y}*y*from a fixed plane can be expressed as a polynomial of

*y*of degree not higher than the third.

A solid is a general prismatoid if

$A_y = a + b_y + cy^2 + dy^3$

Where *a*, *b*, *c*, and *d* are arbitrary constants which may be positive, negative, or zero.

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