Estimating and Costing
If B is the width of formation, d is the height of the embankment, side slope S : 1, for a highway with no transverse slope, the area of cross-section is

B × d - Sd1/2
B + d + Sd
Bd + Sd2
½ (Bd + Sd2)

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Estimating and Costing
The assumption on which the trapezoidal formula for volumes is based, is

The mid-area of a pyramid is half the average area of the ends
The end sections are parallel planes
The volume of the Prismoidal is over-estimated and hence a Prismoidal correction is applied
All listed here

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