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 [math]C = 2\pi r[/math].

[list=1][br][*]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.[br][*]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.[br][*]To find the length of [math]\overline{BC}[/math], first determine the known lengths of [math]\overline{PB}[/math] and [math]\overline{PC}[/math].[br][*]Determine [math]m\angle{CPB}[/math].[br][*]Use trigonometry to find the length of [math]\overline{BC}[/math].[br][*]Determine [math]m\angle{BPD}[/math].[br][*]Use trigonometry to find the length of [math]\overline{BD}[/math] and multiply that value by 2 to find the length of [math]\overline{BC}[/math].[br][*]Find the perimeter of the hexagon.[br][*]Compare the estimate with the calculated circumference of the circle.[br][/list][br][br]This applet is provided by Walch Education as supplemental material for their mathematics programs. Visit [url=http://www.walch.com]www.walch.com[/url] for more information.