Irregular Boundary Area Computation by Simpson's 3/8 Rule

The trapezoidal rule and Simpson's 1/3 rule are the most common methods for computation of the area of irregular boundary. The trapezoidal rule assumes that the irregular boundary is composed of segments of straight lines while Simpson's 1/3 rule assumes parabolic curves. In this paper another approach based on describing the boundary as curves of a third‐degree polynomial is considered. This leads to Simpson's 3/8 rule for which a general formula is developed to give the total area when offsets at equal intervals dividing the area into a multiple of three sections are measured. Practical tests show that this method can give higher accuracy than the methods mentioned for the same amount of field work.