8-3 Perimeter and Circumference
Learn to find the perimeter of a polygon
and the circumference of a circle.
Course 2
8-3 Perimeter
Insert Lesson
Here
and Title
Circumference
Vocabulary
perimeter
circumference
Course 2
8-3 Perimeter and Circumference
The distance around a geometric figure
is its perimeter. To find the perimeter P
of a polygon, you can add the lengths of
its sides.
Course 2
8-3 Perimeter and Circumference
Additional Example 1A: Finding the Perimeter of a
Polygon
Find the perimeter of the polygon.
A.
4 in.
5 in.
4 in.
5 in.
4 in.
P=4+4+5+4+5
P = 22
Use the side lengths.
Add.
The perimeter of the pentagon is 22 in.
Course 2
8-3 Perimeter and Circumference
Additional Example 1B: Finding the Perimeter of a
Polygon
Find the perimeter of the polygon.
B.
25 cm
25 cm
15 cm
P = 25 + 25 + 15
Use the side lengths.
P = 65
Add.
The perimeter of the triangle is 65 cm.
Course 2
8-3 Insert
Lesson
Here
Perimeter
and Title
Circumference
Try This: Example 1A
Find the perimeter of the polygon.
A.
5 in.
4 in.
6 in.
8 in.
P=5+6+8+4
P = 23
Use the side lengths.
Add.
The perimeter of the polygon is 23 in.
Course 2
8-3 Insert
Lesson
Here
Perimeter
and Title
Circumference
Try This: Example 1B
Find the perimeter of the polygon.
B.
25 cm
20 cm
30 cm
P = 25 + 20 + 30
Use the side lengths.
P = 75
Add.
The perimeter of the triangle is 75 cm.
Course 2
8-3 Perimeter and Circumference
You can find the perimeter
of a rectangle by adding
the length of its sides. Or,
since opposite sides of a
rectangle are equal in
length, you can find the
perimeter by using the
formula P = 2l + 2w.
Course 2
w
l
8-3 Perimeter and Circumference
Additional Example 2: Using Properties of a
Rectangle to Find Perimeter
Find the perimeter of a rectangle.
14 ft
18 ft
P
P
P
P
=
=
=
=
2l + 2w
(2 ·18) + (2 ·14)
36 + 28
64
Use the formula.
Substitute for l and w.
Multiply.
Add.
The perimeter of the rectangle is 64 ft.
Course 2
8-3 Insert
Lesson
Here
Perimeter
and Title
Circumference
Try This: Example 2
Find the perimeter of a rectangle.
16 ft
8 ft
P
P
P
P
=
=
=
=
2l + 2w
(2 · 8) + (2 · 16)
16 + 32
48
Use the formula.
Substitute for l and w.
Multiply.
Add.
The perimeter of the rectangle is 48 ft.
Course 2
8-3 Perimeter and Circumference
The distance around a circle is
called circumference. For
every circle, the ratio of
circumference C to diameter d
is the same. This ratio, C , is
d
represented by the symbol ,
called pi. Pi is approximately
equal to 3.14 or 22 . By
7
multiplying both sides of the
equation C =  by d, you get
d
the formula for circumference,
C = d or C = 2r.
Course 2
Radius
Diameter
Circumference
8-3 Perimeter and Circumference
Additional Example 3A: Finding the Circumference
of a Circle
Find the circumference of the circle to the
nearest tenth. Use 3.14 for .
A.
12 in.
C = d
You know the diameter.
C  3.14 · 12 Substitute for  and d.
C  37.68
Multiply.
The circumference of the circle is about 37.7 in.
Course 2
8-3 Perimeter and Circumference
Additional Example 3B: Finding the Circumference
of a Circle
Find the circumference of the circle to the
nearest tenth. Use 3.14 for .
B.
18 cm
C = 2r
You know the radius.
C  2 · 3.14 · 18 Substitute for  and r.
C  113.04
Multiply.
The circumference of the circle is about 113.0 cm.
Course 2
8-3 Perimeter and Circumference
Try This: Example 3A
Find the circumference of the circle to the
nearest tenth. Use 3.14 for .
A.
7 in.
C = d
You know the diameter.
C  3.14 · 7
Substitute for  and d.
C  21.98
Multiply.
The circumference of the circle is about 22 in.
Course 2
8-3 Perimeter and Circumference
Try This: Example 3B
Find the circumference of the circle to the
nearest tenth. Use 3.14 for .
B.
11 cm
C = 2r
You know the radius.
C  2 · 3.14 · 11 Substitute for  and r.
C  69.08
Multiply.
The circumference of the circle is about 69.1 cm.
Course 2
8-3 Perimeter and Circumference
Additional Example 4: Application
The diameter of a circular pond is 42 m. What
is its circumference? Use 22 for .
7
C = d
You know the diameter.
C  22 · 42
7
C  22 · 42
7 1
22 · 42 6
C 7 1
1
C  132
Substitute 22 for  and 42 for d.
7
Write 42 as a fraction.
Simplify.
Multiply.
The circumference of the pond is about 132 m.
Course 2
8-3 Perimeter and Circumference
Try This: Example 4
The diameter of a circular spa is 14 m. What
is its circumference? Use 22 for .
7
C = d
You know the diameter.
C  22 · 14
7
C  22 · 14
7 1
22 · 14 2
C 7 1
1
C  44
Substitute 22 for  and 14 for d.
7
Write 14 as a fraction.
Simplify.
Multiply.
The circumference of the spa is about 44 m.
Course 2
8-3 Perimeter
Insert Lesson
and Title
Circumference
Here
Lesson Quiz
Find the perimeter of each polygon.
1.
8m
12 m
10 m
6m
9m
2.
8 in.
45 m
36 in.
10 in.
3. What is the circumference of a circle with a
a radius of 8 inches? Use 3.14 for . 50.24 in.
4. If a guardrail is to be placed around the edge
of a circular swimming pool with a diameter of
21 ft, how many feet of railing will be needed?
Use 22 for . 66 ft
7
Course 2
Homework
8-3 Worksheet
Study for fraction quiz Thursday