एक प्रिज्मोइड जिसका आधार बहुभुज होते हैं जिनमें समान संख्या होती है और जिनके अन्य चेहरे ट्रेपेज़ॉइड या समांतरोग्राम होते हैं

prismoid's Usage Examples:

- 2 To show that the area of a cross-section of a - prismoid is of the form ax e -{- bx -{- c, where x is the distance of the section from one end, we may proceed as in § 27.

This formula applies to such figures as the cone, the sphere, the ellipsoid and the prismoid.

cot Then volume of prismoid = length X If mini + m2n2 + 2 (m i ne + m270-3a 2 1 tan 0.

In the ordinary case three of the four lateral surfaces of the prismoid are at right angles to the two ends.

Another method of verifying the formula is to take a point Q in the mid-section, and divide up the prismoid into two pyramids with vertex Q and bases ABCD ...

By (i) and (iii), the formula holds for each of these figures; and therefore it holds for the prismoid as a whole.

Then the prismoid is divided into a pyramid with vertex P and base ABCD ..., and a series of tetrahedra, such as PABa or PAab.

(iv) For the prismoid in general let ABCD ...

The most instructive is to regard the prismoid as built up (by addition or subtraction) of simpler figures, which are particular cases of it.

If R and S are the ends of a prismoid, A and B their areas, h the perpendicular distance between them, and C the area of a section by a plane parallel to R and S and midway between them, the volume of the prismoid is *h(A+4C+B).

prismoid's Meaning':

a prismatoid whose bases are polygons having the same number of sides and whose other faces are trapezoids or parallelograms