Thus far, we have dealt with polygons of three and four sides. But there is really no limit to the number of sides a polygon may have. The only practical limit is that unless you draw them on a very large sheet of paper, after about 20 sides or so, the polygon begins to look very much like a circle.

Parts of a regular polygon

In a regular polygon, there is one point in its interior that is equidistant from its vertices. This point is called the **center** of the **regular polygon.** In Figure 1, *O* is the center of the regular polygon.

**Figure 1 **Center, radius, and apothem of a regular polygon.

The **radius** of a regular polygon is a segment that goes from the center to any vertex of the regular polygon.

The **apothem** of a regular polygon is any segment that goes from the center and is perpendicular to one of the polygon's sides. In Figure , *OC *is a radius and *OX *is an apothem.

Finding the Perimeter

Because a regular polygon is equilateral, to find its perimeter you need to know only the length of one of its sides and multiply that by the number of sides. Using *n*‐gon to represent a polygon with *n* sides, and *s* as the length of each side, produces the following formula.

If *p* represents the perimeter of the regular polygon and *a* represents the length of its apothem, the following formula can eventually be shown to represent its area.

**Example 1:** Find the perimeter and area of the regular pentagon in Figure 2, with apothem approximately 5.5 in.

**Figure 2 **Finding the perimeter and area of a regular pentagon.