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:
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-