Agenda
 1st block
 45-45-90 and 30-6090 triangle
worksheet
 Notes 11-4
 Classwork due by end
of class
 3rd block
 Pop quiz
 Go over homework
from Wednesday
night
 Notes 11-4
 Classwork due by end
of class
Areas of Regular Polygons
11-4
Goals/Purpose
• At the completion of the lesson, you will
be able to…
• identify and calculate the center,
radius, apothem, and central angle of a
regular polygon
• Calculate the area of a regular polygon
• We are studying this material because
regular polygons are common in
structures and buildings
Definitions
• Center – the center of the circle circumscribed
about the polygon
• radius – a segment drawn from the center of a
polygon to a vertex
• apothem – a segment drawn from the center of a
polygon that is perpendicular to a side
• central angle – an angle formed by two radii drawn
to consecutive vertices
Theorem 11.6 Area of a Regular
Polygon
• The area of a regular n-gon with side lengths
(s) is half the product of the apothem (a) and
the perimeter (P), so
A = ½ aP, or A = ½ a • ns.
The number of congruent
triangles formed will be
the same as the number of
sides of the polygon.
NOTE: In a regular polygon, the length of each
side is the same. If this length is (s), and
there are (n) sides, then the perimeter P of
the polygon is n • s, or P = ns
More . . .
• A central angle of a regular polygon is
an angle whose vertex is the center and
whose sides contain two consecutive
vertices of the polygon. You can divide
360° by the number of sides to find the
measure of each central angle of the
polygon.
• 360/n = central angle
Ex: Finding the area of a regular
polygon
• A regular pentagon
with radius 1 unit.
Find the area of the
pentagon.
C
1
B
1
D
A
Solution:
• you must find the
apothem (or if the
apothem was given,
you must find the
radius, etc)
• You need to find
measure of central
angle. ABC is
360°/5, or 72°.
B
1
A
D
C
Solution:
• Draw the apothem.
It is an isosceles
triangle so it bisects
the angle.
• You now have a right
triangle and can use
trig ratios to find
the missing sides
B
36°
1
A
D
C
Solution
B
1
A
D
C
You try…..
• Find the area of a regular polygon with
9 sides and a radius of 10
Homework
• Page 442 1-8