Concept Map & Background
Given any circle, one can inscribe a regular polygon of any number of sides within it. The reverse is also true, given any regular polygon, a circle can circumscribe it. We are able to identify relationships between the regular polygon and circle. When a regular polygon is inscribed in a circle, the center of the circle will also be the center of the regular polygon. The radius of the circle will also be the radius of the regular polygon, the distance from the center to a vertex. A central angle of a regular polygon is the angle formed by two radii drawn to consecutive vertices. The apothem of a regular polygon is the (perpendicular) distance from the center of the polygon to a side. The area of a regular polygon is equal to half the product of the apothem and the perimeter. Common formulas used the to find the area of regular polygons includes: A = ½ nsa = ½ ap, where n = the number of sides on the regular polygon, s= the length of the side, a = apothem, p = perimeter. It is important to use apothem when teaching this concept instead of height because that is the terminology on the EOC exam. Students can apply this to help them in solving real world problems.