In many engineering projects, large parcels of land are required for the site and huge amounts of material have to be moved in order to form the necessary embankments, cuttings, foundations, basements, lake and so on. Parcels of land are generally bounded either by straight sides, irregular sides or some combination of both. For these it is usual to calculate their plan areas, that is, the areas contained within their boundaries as they would appear on engineering plans ignoring any undulations in their ground surfaces. In the case of straight-sided areas it is possible to calculate very accurate measurements of their plan areas, whereas in the case of irregular-sided areas only estimated values can be obtained.
Cross-sections are often drawn to help with the volume calculations required for highway construction projects. They can take a number of different forms and they are normally based on longitudinal sections. When drawing cross-sections it is usual to approximate the shape of the ground surface to a series of straight lines. Hence, although accurate measurements of the cross-sectional areas contained within these straight sided boundaries can be made, the values obtained are only estimates of the true cross-sectional areas due to the approximation of the ground surface.