Cool Area of Triangle Problem: Dynamic Construction and Exploration

① This example demonstrates an interesting problem about the area of triangles, using dynamic geometry to visualize relationships among multiple triangles and interior points. ② Core mathematical concepts include triangle area calculation, polygon area, point-in-polygon relationships, and exploring area identities or inequalities through geometric construction. ③ Construction highlights: GeoGebra commands such as Intersect, Point, Polygon, Segment, and PointIn are used to create multiple points (A_1, C, B, etc.), polygons (poly1, poly2, poly3), auxiliary segments, and interior points (Pointpoly1, etc.), allowing dynamic manipulation of points to observe area changes. ④ Suitable for middle or high school geometry classes, math enrichment activities, or as a reference for teachers creating interactive lessons on area and geometric exploration.