Exploring the Area of an Annulus via Concentric Circles

This GeoGebra example demonstrates how to explore the area of an annulus (ring-shaped region) by varying the inner and outer radii of two concentric circles. It focuses on core ideas such as circular geometry, the annulus area relationship A = π(R^2 − r^2), radius identification, and symmetry-based intuition for interpreting the region. Construction is driven by GeoGebra commands and objects from the provided construction summary: “Circle” creates the inner and outer circles (Inner/Small and Outer/Large) with radii r and R; “Point” and “Segment” define key reference points and connecting lines; “Polygon” forms the relevant region boundary(s) such as poly1; and “Area” is used to compute and display the area of the constructed annulus region. The activity is well suited for middle/high school geometry lessons, concept reinforcement, and interactive learning that connects visual area measurement to the standard formula.