Geometric construction of a square equal in area to a given rectangle

This example demonstrates how to construct, using classical geometric construction steps, a square whose area is exactly equal to that of a given rectangle. It centers on the geometric translation of an area condition into a length relationship, turning the requirement “equal areas” into a constructible segment using key points (midpoints, orthogonality) and circle-based intersection geometry. The construction employs core concepts such as area-to-length correspondence, right-angle constraints, and circle/semicircle intersection to determine the needed side length. In GeoGebra, it is built from primitives and relationships: creating points and segments (Point, Segment), forming a semicircle (Semicircle), computing a midpoint (Midpoint), constructing perpendicular lines (OrthogonalLine), finding intersections (Intersect), and assembling the final figures with a polygon outline (Polygon). Objects like the marked key points (e.g., a, b, A, B, C, O, D, E, F) and the polygon/poly1 elements help visualize the rectangle and the constructed equal-area square. Suitable for secondary school geometry lessons and enrichment activities focused on geometric construction and equal-area problems.