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Activity: Areas of Regular Polygons and Circles
Go to: http://www.keypress.com/.../PolygonCircleArea.zip (opens a new window)
Description:

Students manipulate the number of sides in a regular polygon, develop a formula relating the area and perimeter of the polygon, and use their result to develop a formula relating the circumference and area of a circle. The link to the activity itself is to a zip file that contains both the activity in pdf format and the corresponding sketch.

This is a free sample activity from Exploring Geometry with the Geometer's Sketchpad.

Technology Type: Sketchpad 
Author: Key Curriculum Press/Dan Bennett
Language: English 
Cost: Does not require payment for use

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Activity: Exploring Geometry with The Geometer's Sketchpad
Tool: Areas of Regular Polygons and Circles
Courses: Geometry Pi, Regular polygons