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The subject matter evaluates performance in irregular regions extensively applying Newton's Forward Divided Difference Structure, as well as other methods of measurement. Previous work has not looked into the distinctions between genuine and determined amounts for unsymmetrical areas, nor if they succeeded as the number of data points increased; therefore, this investigation forecasts predicted areas, calculates relative mistakes at various locations, and evaluates error cohesiveness. The strategy entails creating tests and using numeric operations, quantitative techniques, as well as the implementation of programs with straightforward screens to properly assess the analysis's correctness. Regardless of knowing that this analysis requires an extensive amount of effort, it provides important insights into practical analytical techniques for innovative area computations by promoting an increased awareness of area estimating workflows, extending student perspectives throughout fundamental algebraic figures, and presenting a fresh approach to area predictions that brings something fresh within the discipline. Results underline the importance of implementing points in reducing inaccuracies showing the stage of converge, validating the dependability of the experiment's achievements, and signaling that the expected region is nearing its exact area. Upcoming study should look at various numerical methodologies that could enhance accuracy while also advancing science in the next wave of higher education.