Download Central angle of a regular polygon

Geometry 11.6
Big Idea: Find Areas of
Regular Polygons
Reminders:
Inscribed polygon: polygon drawn in
the interior of a circle where all
vertices lie on the circle
Regular polygon: a polygon with all
angles and all sides congruent
The center of the
polygon and the
radius of the
polygon are the
center and the
radius of its
circumscribed
circle.
Vocabulary:
Apothem of the polygon:
Perpendicular distance from the
center of the regular polygon to
any side of the polygon
apothem
Vocabulary:
Central angle of a regular polygon:
angle formed by two radii drawn
to consecutive vertices of the
polygon
Measure of Each Central Angle
of a Regular Polygon
To find the measure of
each central angle of a
regular polygon, divide
360° by the number
of sides, n.
360
n
Example: Find each angle measure in
C
ABCDE.
a)
mÐAFB
B
D
G
F
b) mÐAFG
A
c) mÐGAF
E
Theorem 11.11: Area of a
Regular Polygon
Area of a regular n-gon is ½ the
product of the apothem a and
the perimeter P.
aP
A=
2
Example: Find the perimeter and area
of the regular polygon.
6.5
8
Example: Find the perimeter and area
of the regular polygon.
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