Tangent-driven geometry with area links (rhombus and cuboid construction)

This GeoGebra example demonstrates how a tangent-function parameter influences a composite geometry layout: as parameters change, related area relationships in planar triangles and a rhombus become visually traceable through a coordinated, rotatable construction. The key math ideas include tangent/trigonometric modeling of geometric proportions, area connections between triangles and rhombi, and the organization of dimensions for a related cuboid-style parameter set. Construction-wise, it uses GeoGebra commands such as Point to define the controlling points (including paired “primed” counterparts), Polygon to form the main shapes, and Rotate to align or spin parts of the figure so the relationships stay consistent. The object list indicates multiple parameter quantities (length/width/height variables like l, w, h, and a parameter t) and several indexed geometry points (e.g., q1, q2, q4 and their primed variants) that drive the configuration. Interactive buttons and text labels support switching between diagram groups. Suitable for secondary school geometry, integrated function modeling lessons, and classroom demonstrations of linking trigonometry with area reasoning.