Task# Wedges of a Circle

Illustrative MathematicsVaries

The purpose of this task is to help students visualize one way to derive the formula for the area of a circle, which uses the formulas for the circumference of a circle and the area of a parallelogram. The standard asks for 'informal' derivations of this formula, and this task lets students both play and convince themselves. Instructors are encouraged to help any struggling students continue the process by making more drawings (with increasing number of wedges) or by more carefully labeling pieces of the drawing (e.g., the radius). Alternatively, a more hands-on version of this task can be made by having students cut circles into wedges and reassemble the wedges themselves.