Volumes
 Cross Sections
 End Area Method
 Prismoidal Formula
 Rectangular Base Method
 Triangular Base Method
 Balance of Cut and Fill
 Volumes From Contours
 Digital Terrain Models

Triangular Base Method

Triangular elements can better define the surface because any three levels will define a plane where as four levels (in the general case) will only define a warped non planar surface.

In this case the area will become (s²/2). Then the total volume as made up of a series of prisms on triangular bases and be developed by,

V1 = (h₁ + h₂ + h₆) s²/6

For the second and third elements the volumes are,

V2 = (h₂ + h₆ + h₇) s²/6

V3 = (h₂ + h₃ + h₇) s²/6

The total volume of the area covered by the entire grid of levels is,

V = [V₁ + V₂ + V₃ + ............. + V_n]

and therefore the volume in general terms may be expressed as,

where N_i is the occurrence number,

h_i is the height difference at each point,

s² the area of the square grid element,

Of course the occurrence numbers will change from the previous case of the rectangular prisms .

Volumes from spot heights is convenient but is generally restricted to small areas since the setting out and levelling of a large grid can be extremely tedious and time consuming. The use of triangles rather than rectangles will usually increase the accuracy slightly, though it will tend to increase the amount of arithmetic involved.