Comparing Figure Sizes by Cutting and Pasting (Problem 3)

This GeoGebra applet demonstrates how to compare the areas of different geometric figures by cutting and pasting polygons. Through a series of interactive, dynamically animated steps, the applet shows students how polygons can be dissected and reassembled to reveal relationships between areas. Commands such as Polygon and Midpoint are used to construct the figures and guide the transformation process, ensuring precision in each cut and rearrangement. The applet visually presents the step-by-step procedure of area-preserving transformations, making the abstract concept of conservation of area tangible and intuitive. At each stage, learners can observe how a complex shape is broken into smaller pieces and then recombined into a new configuration whose area can be more easily compared with another figure. This approach reinforces the key mathematical principle that the total area of a figure remains unchanged when it is cut into parts and reassembled, regardless of the final arrangement. The interactive nature of the applet allows users to control the pace and sequence of the demonstration, pausing at critical moments to reflect on what has changed and what has remained constant. Designed primarily for geometry instruction, the applet serves as a powerful visual aid that bridges the gap between concrete manipulation and formal reasoning about area. It is particularly useful in helping students develop spatial reasoning skills and build a solid conceptual foundation before moving on to area formulas and proofs. By engaging with the applet, learners gain confidence in using dissection strategies as a problem-solving tool, an essential technique in geometry. The Chinese title "以剪贴比较图形大小（题3）" identifies this as the third problem in a series, suggesting it is part of a structured set of activities designed to progressively build understanding of area comparison through transformation. Overall, this GeoGebra applet combines interactivity, visual clarity, and mathematical rigor to support effective geometry education.