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Lesson 1-6
Polygons
Lesson 3-4: Polygons
1
Polygons
Definition: A closed figure formed by a finite number of coplanar
segments so that each segment intersects exactly two
others, but only at their endpoints.
These figures are
These figures are
Lesson 3-4: Polygons
2
Classifications of a Polygon
: No line containing a side of the polygon contains a point
in its interior
:
A polygon for which there is a line
containing a side of the polygon and
a point in the interior of the polygon.
Lesson 3-4: Polygons
3
Classifications of a Polygon
:
A convex polygon in which all interior angles have the
same measure and all sides are the same length
:
Two sides (or two interior angles) are not congruent.
Lesson 3-4: Polygons
4
Polygon Names
3 sides
Triangle
4 sides
Quadrilateral
5 sides
Pentagon
6 sides
Hexagon
7 sides
Heptagon
8 sides
Octagon
9 sides
Nonagon
10 sides
Decagon
12 sides
n sides
Dodecagon
n-gon
Lesson 3-4: Polygons
5
Perimeter of a Polygon
The perimeter of a polygon is the sum of the lengths of its sides,
which are segments.
s
l
a
b
s
w
w
l
s
s
c
Rectangle
Triangle
P=a+b+c
P=w +l+w+l
P = 2w + 2l
Square
P=s+s+s+s
P = 4s
Reminder: distance formula
distance  ( x2  x1 )2  ( y2  y1 )2
Lesson 3-4: Polygons
6
Name each polygon by its number of
sides. Then classify it as convex or
concave and regular or irregular.
1.
2.
Lesson 3-4: Polygons
7
A landscape designer is putting black plastic edging around
a rectangular flower garden that has length 6.4 meters and width 5.7 meters.
The edging is sold in 5-meter lengths.
A) Find the perimeter of the garden and
determine how much edging the
designer should buy.
B) Suppose the length and width of
the garden are tripled. What is the
effect on the perimeter and how
much edging should the designer
buy?
Lesson 3-4: Polygons
8
Find the perimeter of triangle ABC if
A(4, 4), B(-4, 2) and C(3, -3).
Lesson 3-4: Polygons
9
Use Perimeter to Find Sides

The length of a rectangle is five times the width. The perimeter is
4 yards. Find the length of each side.
Lesson 3-4: Polygons
10
Find the length of each side of the
regular polygon for the given perimeter.
P = 120 meters
P = 156 feet
Lesson 3-4: Polygons
P = 81 inches
11