Question

Distinguish between trapezoidal and prismoidal rule

Answer 1

1) Prismoidal Formula:

This formula is based on the assumption that A1 and A2 are the areas at the ends and Am is the area of mid section parallel to ends, L=Length between the ends.

From mensuration, volume of a prism having end faces is in parallel planes:

V=L/6*(A1+A2+4Am)

This is known as prismoidal formula.

2) Trapezoidal formula:

It is also known as average are or mean sectional are formula. This method is based is based on the assumption that the mid area of a pyramid is half the average area of the ends and the end sections are in parallel planes.

If A1 and A2 are areas of the ends and L is the length between two sections the volume of the prismoid is given by-

V=L/2(A1+A2) or V=LAm Am=mean sectional area.