Area Problem: Random Polygons and Binomial Distribution Simulation

① This example demonstrates a visual problem involving area calculation combined with probability and statistics, where random polygons are generated and their areas are computed. ② Core mathematical concepts include area, subtraction, logic, binomial distribution, confidence intervals, and stochastic processes, highlighting mathematical modeling and statistical simulation. ③ Construction details: The GeoGebra commands used include Random to generate random points, Polygon to construct polygons, Sequence to create sequences, and Textfield for input boxes; objects include point A, side, polygons poly1 and poly2, functions f, g, h, i, lists list1 and list2, a button button1 to trigger calculations, and text boxes text1, text2, text3, and answerbox for output. ④ Suitable for high school and above, this example serves as an interactive tool for exploring the relationship between area and probability, or as a teaching aid for statistical simulation and experimental mathematics.