Download of sides

# of
sides
# of
triangles
Sum of
measures of
interior angles
3
1
1(180)=180
4
2
2(180)=360
5
3
3(180)=540
6
4
4(180)=720
n
n-2
(n-2) • 180
If a convex polygon has n sides,
then the sum of the measure of
the interior angles is
(n – 2)(180°)
If a regular convex polygon
has n sides, then the measure
of one of the interior angles is
(n  2)180
n
Ex. 1 Use a regular 15-gon to answer the questions.
A)Find the sum of the measures of the
interior angles. 2340°
B) Find the measure of ONE interior angle
156°
Ex: 2 Find the value of x in the polygon
x
126
130
100
143
117
126 + 130 + 117 + 143 + 100 + x = 720
616 + x = 720
x = 104
Ex: 3 The measure of each interior angle is 150°,
how many sides does the regular polygon have?
(n  2)  180
 One interior angle
n
(n  2)  180
 150
n
(n  2)180  150n
180n  360  150n
30n  360
n  12
A regular
dodecagon
Two more important terms
Interior
Angles
Exterior
Angles
The sum of the
measures of the
exterior angles of a
convex polygon, one
at each vertex, is 360°.
2
1
3
5
4

m1  m2  m3  m4  m5  360
The sum of the
measures of the
exterior angles of a
convex polygon, one
at each vertex, is 360°.
1
3
2

m1  m2  m3  360
The sum of the
measures of the
exterior angles of a
convex polygon, one
at each vertex, is 360°.
1
2
4
3

m1  m2  m3  m4  360
The measure of each exterior
angle of a regular polygon is
360
n
Ex. 4 Find the measure of ONE exterior angle of a
regular 20-gon.
sum of the exterior angles

number of sides
360

20
18°
Ex. 5 Find the measure of ONE exterior angle of a
regular heptagon.
sum of the exterior angles

number of sides

360

7
51.4°
Ex. 6 The sum of the measures of five interior
angles of a hexagon is 625. What is the measure of
the sixth angle?
95°
Let’s practice!
11.1 Worksheet
Area of an Equilateral Triangle
30 30
s
s
60
60
s
1
2
A
3s
4
Ex: 1 Find the area of an equilateral triangle with 4 ft
sides.
A  .25 34
1
2
A
3s
4
2
A  6.93 ft
2
A Circle can be circumscribed around any regular polygon
VERTICES
360
n
A Central
Angle
is an
whose
vertex
A RADIUS
joins
theangle
center
of the
is the polygon
center and
two
regular
withwhose
any ofsides
the are
vertices
consecutive radii
A Regular Hexagon
Equal Sides
Equal Angles
s
How many equilateral triangles make
up a regular Hexagon?
What is the area of each triangle?
1
2
A
3s
4
What is the area of the hexagon?
6 • (the area of the triangle)
41.569
What is the area of
this regular hexagon?
units2
4
1
A
3s 2
4
The area of an equilateral triangle
A = 6.9282 The area of our equilateral triangle in this example
How many identical equilateral triangles do we have? 6
A = 6 * (6.9282)
The area of our hexagon in this example
An APOTHEM is
the distance
between the
center and a
side. (It MUST
be perpendicular
to the side.)
How to find the
You need to know the
apothem and perimeter
Area = (1/2)•a•P
or A = .5•a•P
Area of a Regular Polygon:
A = ½ aP
A = .5 (apothem) (# of sides)(length of each side)
a
A Regular Octagon
7 ft
360/8=45
22.5°
45
x
7
3.5 ft
Perimeter is 56 feet
Apothem is 8.45 feet
7 ft
What is the area?
Area = .5 • 8.45 • 56
Area = 236.6
2
ft
11.2 Worksheet
Practice B ODDS
Worksheets’
EVENS