Shape 

Copyright David & Cynthia Thomas, 2009

Circumference & Area of Circles--Directed Activity: The Area of a Circle

Directed Activity                    The Area of a Circle                                                             

Focus	Estimating the area of a circle.
Technologies	The Geometers Sketchpad and model 3_CircleArea.gsp.
Background	Using model 3_CircleArea.gsp, (See Figure 3.33) vary the size of the sector used to approximate a rectangle having the same area as the circle. For instance, if the central angle is adjusted to 30°, the top right vertex of the rectangle must be adjusted to coincide with the top right vertex of the sixth yellow sector (Why?).      Figure 3.33: Estimating the Area of a Circle
Tasks	· Perform this procedure for the following central angles, recording the height and area data for each: 45°, 30°, 20°, 12°. · As the central angle gets smaller, what happens to the … - Height relative to the radius? - Rectangle area relative to the circle area? · Use this model to justify the area formula for a circle, .