Section 7.3 Regular Polygons and Area A regular polygon is both equilateral and equiangular. 9/18/2018 Section 7.3 Nack

To construct a circle inscribed in a square: Construction 1 To construct a circle inscribed in a square: The Center O must be the point of concurrency of the angle bisectors of the square. Construct the angle bisectors of two adjacent vertices to find O. From O, construct OM perpendicular to a side. The length of OM is the radius. Diagrams p. 357 Figure 7.32 9/18/2018 Section 7.3 Nack

Given a regular hexagon, construct a circumscribed  X. Construction 2 Given a regular hexagon, construct a circumscribed  X. The center of the circle must be equidistance from each vertex of the hexagon. Construct two perpendicular bisectors of two consecutive sides of the hexagon The Center X is the point of concurrency of these bisectors. The length from X any vertex is the radius of the circle. Diagrams p. 357 Figure 7.33 9/18/2018 Section 7.3 Nack

A radius of a regular polygon is any line segment that joins the Definitions The center of a regular polygon is the common center for the inscribed and circumscribed circles of the polygon. A radius of a regular polygon is any line segment that joins the center of the regular polygon to one of its vertices. 9/18/2018 Section 7.3 Nack

An apothem of a regular polygon is any line segment drawn from the center of that polygon perpendicular to one of the sides. A central angle of a regular polygon is an angle formed by two consecutive radii of the regular polygon. 9/18/2018 Section 7.3 Nack

Theorems Theorem 7.3.1: A circle can be circumscribed about (or inscribed in) any regular polygon. Theorem 7.3.2: The measure of the central angle of a regular polygon of n sides is given by c = 360/n. Theorem 7.3.3: Any radius of a regular polygon bisects the angle at the vertex to which it is drawn. Theorem 7.3.4: Any apothem of a regular polygon bisects the side of the polygon to which it is drawn. 9/18/2018 Section 7.3 Nack

Area of a Regular Polygon Theorem 7.3.5: The area A of a regular polygon whose apothem has length a and whose perimeter P is given by: A = ½ aP. 9/18/2018 Section 7.3 Nack