A Mathematical Model for Estimating the Area of a Large Leaf

Abstract

A mathematical model for estimating the area of large leaves was developed and validated with the leaves of plantain (<i>Musa paradisiaca</i>). The length of each plantain leaf was characterized by the mid-rib length which was divided into a certain number of equal parts of length. By this divisions, two major geometrical shapes were obtained, viz; trapezoidal shapes bounded by half elliptical shapes at the two ends of the leaf. In this work, the mathematical expression for the surface area of a plantain leaf was obtained by summing the areas of the trapeziums and the two half ellipses. The values of leaf areas as generated from this model for various seizes of plantain leaves converged reasonably well with true values obtained by the weighing method of same plantain leaf seizes. The correlation between these two values was carried out to ascertain the fitness of the mathematical model as developed here showed a linear relationship for the various mid-rib divisions tested in this study. It is thus concluded here that once the calculated area of the large leaf is known for a specific number of divisions with this model, the true area can be estimated. The main advantages of the new method are precision, accuracy, and applicability to determine the area of large leaves far out in the field where electrical weighing balance and large graph papers are not available.