Area means of terrestrial gravity and geoid height are often often formed from data and used to compute spherical harmonic potential coefficients. One commonly used area shape is the trapezoid, formed with sides corresponding to meridians of latitude and parallels of longitude. Data averaging modifies the spectrum of spherical harmonic coefficients. Explicit closed formulas are given for the relation between the surface harmonic of an unsmoothed and that of a smoothed function, illustrating the smoothing and aliasing due to averaging. The unaveraged coefficients can be calculated, but the aliasing remains. Also shown is that no arbitrary relation exists between the block size of an area and the degree of the corresponding spherical-harmonic representation.