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] [*]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 [math]\overline{BC}[/math], first determine the known lengths of [math]\overline{PB}[/math] and [math]\overline{PC}[/math]. [*]Determine [math]m\angle{CPB}[/math]. [*]Use trigonometry to find the length of [math]\overline{BC}[/math]. [*]Determine [math]m\angle{BPD}[/math]. [*]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]. [*]Find the perimeter of the hexagon. [*]Compare the estimate with the calculated circumference of the circle. [/list] This applet is provided by Walch Education as supplemental material for the [i]UCSS Secondary Math II[/i] program. Visit [url="http://www.walch.com"]www.walch.com[/url] for more information on our resources.