1.6 POLYGONS
Objectives
Identify and name polygons.
 Find perimeters of polygons.

Polygons

Polygon – a closed figure whose sides
are formed by a finite number of coplanar
segments
 We name a polygon by using the letters of
its vertices, written in consecutive order.
Y
P
A
C
B
D
T
X
Q
R
U
W
V
Types of Polygons

If the lines of any segment of the polygon
are drawn and any of the lines contain
points that lie in the interior of the
polygon, then it is concave.

Otherwise, it is convex (no points of the
lines are in the interior).
Classifying Polygons

Polygons are classified by the number of sides they
have. A polygon with n number of sides is an n-gon.
Polygon
Triangle
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Number of Sides
3
4
5
6
7
8
9
10
Regular Polygons

A convex polygon in which all of the sides and all
of the angles are congruent is called a regular
polygon.
Example 1a:
Name the polygon by its number of sides. Then
classify it as convex or concave, regular or irregular.
There are 4 sides, so this is a quadrilateral.
No line containing any of the sides will pass through the
interior of the quadrilateral, so it is convex.
The sides are not congruent, so it is irregular.
Example 1b:
Name the polygon by its number of sides. Then
classify it as convex or concave, regular or irregular.
There are 9 sides, so this is a nonagon.
A line containing some of the sides will pass through the
interior of the nonagon, so it is concave.
The sides are not congruent, so it is irregular.
Name each polygon by the number of sides. Then
classify it as convex or concave, regular or irregular.
a.
b.
Perimeter
The perimeter of a polygon is the sum of
all of the lengths of its sides.
 There are a few special formulas for some
polygons (i.e. a square’s perimeter is
equal to 4s with s equaling the measure
of a side and a rectangle’s perimeter is
equal to 2l + 2w with l equaling the
length and w representing the width of
the rectangle).

Example 2a:
CONSTRUCTION
A masonry company is contracted to lay three
layers of decorative brick along the foundation for a
new house given the dimensions below. Find the
perimeter of the foundation and determine how
many bricks the company will need to complete the
job. Assume that one brick is 8 inches long.
Example 2a:
First, find the perimeter.
of the sides.
The perimeter of the foundation is 216 feet.
Example 2a:
Next, determine how many bricks will be needed to
complete the job. Each brick measures 8 inches, or
Divide 216 by
foot.
to find the number of bricks needed for
one layer.
Answer: The builder will need 324 bricks for each layer.
Three layers of bricks are needed, so the
builder needs 324 • 3 or 972 bricks.
Example 2b:
CONSTRUCTION
The builder realizes he accidentally halved the size of
the foundation in part a. How will this affect the
perimeter of the house and the number of bricks the
masonry company needs?
Example 2b:
The new dimensions are twice the measures of the
original lengths.
The perimeter has doubled.
The new number of bricks needed for one layer is
or 648. For three layers, the total number of
bricks is 648 • 3 or 1944 bricks.
Answer: The perimeter and the number of bricks
needed are doubled.
SEWING Miranda is making a very unusual quilt. It is in
the shape of a hexagon as shown below. She wants to
trim the edge with a special blanket binding.
The binding is sold by the yard.
a. Find the perimeter of the
quilt in inches. Then
determine how many yards
of binding Miranda
will need for the quilt.
yd
SEWING Miranda is making a very unusual quilt. It is in
the shape of a hexagon as shown below. She wants to
trim the edge with a special blanket binding.
The binding is sold by the yard.
b. Miranda decides to make
four quilts. How will this
affect the amount of
binding she will need? How
much binding will she need
for this project?
Answer: The amount of binding is multiplied by 4.
She will need
yards.
Example 3:
Find the perimeter of pentagon ABCDE with A(0, 4),
B(4, 0), C(3, –4), D(–3, –4), and E(–3, 1).
Example 3:
Use the Distance Formula,
to find AB, BC, CD, DE, and EA.
,
Example 3:
Answer: The perimeter of pentagon ABCDE is
Find the perimeter of quadrilateral WXYZ with
W(2, 4), X(–3, 3), Y(–1, 0), and Z(3, –1).
Example 4:
The width of a rectangle is 5 less than twice its length.
The perimeter is 80 centimeters. Find the length of each
side.
Let
represent the length. Then the width is
.
Example 4:
Perimeter formula for rectangle
Multiply.
Simplify.
Divide each side by 6.
The length is 15 cm. By substituting 15 for ,
the width becomes 2(15) – 5 or 25 cm.