Open-Middle Trapezoid Area Under Fixed Perimeter (GeoGebra)

This example demonstrates an “open middle” trapezoid area selection problem: under a fixed perimeter, how the trapezoid’s area can vary as geometric parameters change, and how the admissible configurations can be constructed and compared. It centers on trapezoid geometry with perimeter constraints, relationships between area and geometric invariants, angle measurement (e.g., α, β, γ, δ), midpoint/segmentation constructions, and encoding constraints with a conic (ellipse) to convert the area question into an intersection/parameter construction problem. Construction uses Intersect to obtain key points, Point/Segment/Ray to build edges and rays, Ellipse to represent the locus of configurations satisfying the constraint, Polygon to outline the trapezoid, PointIn and Midpoint for membership and midpoint placement, Rotate and Angle to control orientations and required angles, and SurdText/Textfield for readable parameter and algebraic-style annotations. Suitable for high school advanced geometry, contest preparation, and interactive teaching about constrained optimization by geometric loci.