Regular polygons are common in Geometry. This lesson begins with [br]demonstrating examples of some common regular polygons. All polygons have[br] a center which with regular polygons allow us to circumscribe or [br]inscribe a circles with the polygon. The radius of the circumscribed [br]circle is from this center to a vertex of the polygon. The distance from[br] the center of the polygon to the midpoint of a side is called the [br]apothem, or the radius of the inscribed circle.

Excellent Resource: [url=http://www.mathopenref.com/polygonregular.html]http://www.mathopenref.com/polygonregular.html[/url][br][br]Names of Polygons: [url=https://www.mathsisfun.com/geometry/polygons.html]https://www.mathsisfun.com/geometry/polygons.html[/url][br][br]This lesson can be extended to "Looking at LTF Polygons in a Circle", [br]this applet will assist in completing the exercise.[br][br]The circle on the screen is a unit circle; however, you can change the [br]radius to match any value you measure up to 8 units. The table will give[br] the results up to a 100-gon.[br][br]Table format from LTF activity on Limits of a Polygon in a Circle.[br][br]Triangle ABC is triangle formed by the point A and any side of the [br]polygon. The area of the polygon is the number of sides times the area [br]of Triangle ABC.[br][br]If you expand the radius of the circle and can no longer see the figure,[br] click mouse on point A and scroll the figure in and out...[br][br][url=https://my.nctm.org/network/members/profile?UserKey=dcf645bd-737a-427a-9cce-109ab4505760]Fred Gustavson[/url] suggest to refer to Archimedes on this subject. He circumscribed and inscribed [br]regular polygons sides 6 to 96 in doubling steps around a circle. By direct computation he showed that [br] 3 10/71<π<3 1/7.