Warm-Up
Exercises
Bell Work
1. An isosceles triangle has side lengths 20 meters,
26 meters, and 26 meters. Find the length of the
altitude to the base.
2. Solve 18 = 12
x.
3. Evaluate (4 cos 10º)(10 sin 20º).
4. Evaluate
10 .
tan 88º
Warm-Up
Exercises
Notes
Definitions
Center of the Polygon
Center of the circumscribed circle.
Radius of the Polygon
Radius of the circumscribed circle.
Warm-Up
Exercises
Notes
Definitions
Apothem of the Polygon
The distance from the center to
any side of the polygon.
Central Angle of a regular polygon
Angle formed by two radii drawn to consecutive vertices
of the polygon. (360° divided by the # of sides)
Warm-Up1Exercises
EXAMPLE
In the diagram, ABCDE is a regular
pentagon inscribed in F. Find
each angle measure.
a.
m
AFB
Warm-Up1Exercises
EXAMPLE
In the diagram, ABCDE is a regular
pentagon inscribed in F. Find
each angle measure.
b.
m
AFG
Warm-Up1Exercises
EXAMPLE
In the diagram, ABCDE is a regular
pentagon inscribed in F. Find
each angle measure.
c.
m
GAF
Warm-Up
Exercises
GUIDED
PRACTICE
In the diagram, WXYZ is a square inscribed in
1.
Identify the center, a radius,
an apothem, and a central
angle of the polygon.
P.
Warm-Up
Exercises
GUIDED
PRACTICE
2.
Find m
XPY, m
XPQ, and m
PXQ.
Warm-Up
Exercises
Notes
Area of an n-gon
Warm-Up
Exercises
Notes
Area of a Regular Polygon
The area of a regular n-gon with side length s is one half
the product of the apothem a and the perimeter P.
A = ½ a·P or
A = ½ a·n·s
Warm-Up2Exercises
EXAMPLE
You are decorating the top of a
table by covering it with small
ceramic tiles. The table top is
a regular octagon with 15 inch
sides and a radius of about
19.6 inches. What is the area
you are covering?
Warm-Up3Exercises
EXAMPLE
A regular nonagon is inscribed in a circle with
radius 4 units. Find the perimeter and area of the
nonagon.
Warm-Up
Exercises
GUIDED
PRACTICE
Find the perimeter and the area of the regular polygon.
3.
Warm-Up
Exercises
GUIDED
PRACTICE
Find the perimeter and the area of the regular polygon.
4.
Warm-Up
Exercises
GUIDED
PRACTICE
Find the perimeter and the area of the regular polygon.
5.
Warm-Up
Exercises
Notes
Summary
To find the length of a regular n-gon with radius r, you
may need to first find the apothem a or side length s.
We can use:
- Pythagorean Theorem
- Special Right Triangles
- Trigonometry
Warm-Up
Exercises
Daily
Homework
Quick
CheckQuiz
1.
Find the measure of the central angle of a
regular polygon with 24 sides.
Find the area of each regular polygon.
2.
Warm-Up
Exercises
Daily
Homework
Quick
CheckQuiz
3.
Warm-Up
Exercises
Daily
Homework
Quick
CheckQuiz
Find the perimeter and area of each regular polygon.
4.
Warm-Up
Exercises
Daily
Homework
Quick
CheckQuiz
5.
Warm-Up
Exercises
For Tomorrow
Homework
HW: 11.3 (pg. 729-731) #6,16,20,24,28,31-33,37