Exploring the Perimeter and Area of Rectangles

This GeoGebra example dynamically explores the relationship between the side lengths of a rectangle and its perimeter and area. The core mathematical concepts include the formulas for perimeter ($P = 2(a+b)$) and area ($S = a imes b$), bridging geometric intuition with algebraic calculation. In terms of construction, it utilizes the `OrthogonalLine` command to draw perpendicular sides, `Intersect` to locate vertices A, B, C, and D, and the `Polygon` command to form the rectangle `poly1`. Interactive features are implemented via `Textfield` and `InputBox` for user inputs, while `Perimeter` and `PointIn` commands handle the real-time computation and visual rendering of geometric properties. This tool is ideal for middle school students, beginner high school learners, or mathematics educators seeking an interactive visual aid for basic geometry and algebraic formulas.