Grade 6: Derivation of the Area Formula of a Circle

This GeoGebra applet dynamically demonstrates the derivation of the circle area formula for Grade 6 students. By dividing a circle into a given number of equal sectors and applying geometric transformations such as rotation, translation, and interlocking拼接, the sectors are rearranged to form an approximate rectangle. As the number of sectors increases, the jagged edges become progressively smoother, and the resulting shape converges toward a perfect rectangle. This visual process provides an intuitive understanding of the limit concept underlying the formula S = πr². The applet allows students to interactively adjust the number of sectors, observe how the approximation improves, and see the relationship between the rectangle's dimensions and the circle's radius and circumference. The length of the rectangle corresponds to half the circumference of the circle (πr), while its width equals the radius (r), leading directly to the area formula. This interactive demonstration helps students grasp the powerful idea that geometric transformations can preserve area while changing shape, and introduces the foundational notion of limits in a concrete and accessible way. The tool is particularly effective for visual learners and reinforces the connection between circular and rectangular geometry.