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prismatoid : ウィキペディア英語版
prismatoid
In geometry, a prismatoid is a polyhedron where all vertices lie in two parallel planes. Its lateral faces can be trapezoids or triangles.〔William F. Kern, James R Bland,''Solid Mensuration with proofs'', 1938, p.75〕 If both planes have the same number of vertices, and the lateral faces are either parallelograms or trapezoids, it is called a prismoid.
== Area==
If the areas of the two parallel faces are A1 and A3, the cross-sectional area of the intersection of the prismatoid with a plane midway between the two parallel faces is A2, and the height (the distance between the two parallel faces) is h, then the volume of the prismatoid is given by V = \frac or V = \frac(This formula follows immediately by integrating the area parallel to the two planes of vertices by Simpson's rule, since that rule is exact for integration of polynomials of degree up to 3, and in this case the area is at most a quadratic function in the height.)

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