Math in Our World
Section 10.3
Polygons and Perimeter
Learning Objectives
 Find the sum of angle measures of a polygon.
 Find the angle measures of a regular polygon.
 Find the perimeter of a polygon.
Polygons
Closed geometric figures whose sides are
line segments are classified according to
the number of sides. These figures are
called polygons.
Polygons
Sum of the Angle Measures
The sum of the measures of the angles of a
polygon with n sides is (n – 2)180°.
EXAMPLE 1
Finding the Sum of Angle
Measures of a Polygon
Find the sum of the measures of the angles of a
heptagon.
SOLUTION
A heptagon has seven sides, so the sum of the measures
of the angles of the heptagon is
The sum of the measures of the angles of a heptagon is
900°.
Quadrilaterals
Just as there are special names for certain
types of triangles, there are names for
certain types of quadrilaterals as well.
A trapezoid is a quadrilateral
that has exactly two parallel
sides.
A parallelogram is a
quadrilateral in which opposite
sides are parallel and equal in
measure.
Quadrilaterals
A rectangle is a parallelogram
with four right angles.
A rhombus is a parallelogram
in which all sides are equal in
length.
A square is a rhombus
with four right angles.
Relationship of the Quadrilaterals
Looking at the relationships, you
can see that a square is also a
rectangle and a rhombus. A
rhombus and a rectangle are
also parallelograms.
Regular Polygons
In a regular polygon all of the sides have
the same length, and all of the angles are
equal in measure.
The most common examples of regular
polygons are squares and equilateral
triangles.
EXAMPLE 2
Finding Angle Measure for a
Regular Polygon
Find the measure of each angle of a regular
hexagon.
SOLUTION
First, find the sum of the measures of the angles for a
hexagon. The formula is (n – 2)180°, where n is the
number of sides.
Since a hexagon has six sides, the sum of the measures of
the angles is (6 – 2)180° = 720°.
Next, divide the sum by 6 since a hexagon has six angles:
720° ÷ 6 = 120°.
Each angle of a regular hexagon has a measure of 120°.
Perimeter
The perimeter of a polygon is the sum of the
lengths of its sides.
EXAMPLE 3
Finding the Perimeter of a
Rectangle
The Houser family finds their dream home perfect
in every way except one: the backyard is not
fenced in, and their dog Bunch needs room to
roam. The rectangular portion they plan to enclose
is 95 feet wide and 70 feet long. How much fence
will they need to enclose the yard on all four
sides?
EXAMPLE 3
Finding the Perimeter of a
Rectangle
SOLUTION
The amount of fence needed is the perimeter of the
rectangle.
The Housers need 330 feet of fence.
EXAMPLE 4
Finding the Perimeter of a
Polygon
The length of each outside wall of the Pentagon is
921 feet. Suppose that a sentry must walk the
outside wall six times during his 4-hour shift. How
many miles does he walk in one shift?
SOLUTION
A pentagon has five sides, and each has length 921 feet,
so the sum of the lengths of the sides is 5 x 921 = 4,605 ft.
In walking the perimeter six times, the sentry covers
6 x 4,605 = 27,630 feet. Now we convert to miles:
27, 630 ft
1mi

 5.23 miles
5, 280 ft
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