The center of a regular polygon is the center of the circumscribed circle.
Pt. O is the center of regular pentagon ABCDE.
A B
E C
D
O
The radius of a regular polygon is a segment connecting its center with a vertex.
is a radius of
regular pentagon
.
OB
ABCDE
A B
E C
D
O
How many radii does a regular pentagon have?
5 radii
How many radii will any regular polygon have?
The number of sides
An apothem of a regular polygon is the distance from the center to the side of the regular polygon.
is an apothem
of regular pent.
.
OF
ABCDE
A B
E C
D
O
F
A central angle of a regular polygon is an angle whose vertex is the center of the polygon and whose sides contains consecutive vertices of the polygon.
is a central angle
of regular pentagon .
AOB
ABCDE
A B
E C
D
O
1. Draw a regular triangle, a regular quadrilateral, and a regular hexagon.
2. Draw all the central angles of each of the regular polygons.
3. What must be true of all central angles of a regular polygon and what is the sum of these angles?
They are congruent.
Their sum is 360 .
4. Find the measure of one central angle of each of the regular polygons from #1.
regular triangle is 120°
regular quadrilateral is 90°
regular hexagon is 60°
5. Find measure of one central angle of a regular n-gon.
measure of one central angle
360of a regular gon = n
n
Example 1
Find the measure of a central angle of the following regular polygons:
a) a regular pentagon
36072
5
Area of a Regular Polygon
The area of a regular polygon is half the product of the apothem and the perimeter of the regular polygon.
Example 3Find the area of each of the following regular polygons.
2
13 3 54
2
81 3 in
A
1. a regular triangle with a side length of 18 in.
18 in.
a30
9
93 3
3 a
3 18 54 P
2. a regular quadrilateral with a side length of 12 ft. using the area of a regular polygon formula
45a
12 ft.
6
6a
4 12 48 P
2
16 48
2
144 ft.
A
Example 4Find the area of a regular octagon with side length of 14 cm to the nearest centimeter.
14 cm
722.5
a
tan 22.57
a
7 tan 22.5 a2.9a
8 14 112 P
212.9 112 162 cm.
2 A
Top Related