Show how the perimeter of a hexagon can be used to find an estimate for the circumference of a circle that has a radius of 5 meters. Compare the estimate with the circle’s perimeter found by using the formula .

Draw a circle and inscribe a regular hexagon in the circle. Find the length of one side of the hexagon and multiply that length by 6 to find the hexagon’s perimeter.

Create a triangle with a vertex at the center of the circle. Draw two line segments from the center of the circle to vertices that are next to each other on the hexagon.

To find the length of , first determine the known lengths of and .

Determine .

Use trigonometry to find the length of .

Determine .

Use trigonometry to find the length of and multiply that value by 2 to find the length of .

Find the perimeter of the hexagon.

Compare the estimate with the calculated circumference of the circle.

This applet is provided by Walch Education as supplemental material for the CCGPS Analytic Geometry program. Visit www.walch.com for more information on our resources.