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
1 ,
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.
Finding the Area
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.
|
|
|
Fundamental Ideas
Perimeter and Area
