Geometric Construction of Regular Polygon Area

This example demonstrates how to construct a regular polygon with a chosen number of sides n, then express and visualize its area via geometric decomposition. It focuses on concepts such as central angles (θ), symmetry-based partitioning into congruent triangles, and area relationships derived from segment heights and ratios. Construction highlights include: using Sequence to generate vertices, Polygon to draw the regular polygon, OrthogonalLine to build perpendiculars for key height measurements, and Intersect to locate crucial intersection points that define the subregions. The model employs Angle to mark the central/related angles, Rotate to replicate symmetric features around the center, and Circle together with Segment to support the geometric scaffolding. Textfield/Text label intermediate quantities (e.g., a, b, s, c, θ) so students can track how the area components relate. Suitable for middle/high school geometry, classroom demonstrations, and parameterized geometric reasoning.