9-2 Perimeter and Circumference
Warm Up
Problem of the Day
Lesson Presentation
Course 2
9-2 Perimeter and Circumference
Warm Up
Add or multiply.
1. 8.2 + 5.6 + 8.2 + 5.6 27.6
2. 12.4 + 15.8 + 9.3
37.5
3. 22 · 3.14
69.08
Course 2
9-2 Perimeter and Circumference
Problem of the Day
A rectangular piece of sheet metal
measures 5 in. by 6 in. A rectangular
notch 1 in. deep and 7 in. wide is cut
64
out of the middle of each side. What is
the perimeter of the piece after the
cuts have been made? (Hint: You don’t
have to use fractions.)
30 in. (the original 6 in. by 5 in. sheet
plus 8 in. for the eight 1 in. cuts)
Course 2
9-2 Perimeter and Circumference
Learn to find the perimeter of a polygon
and the circumference of a circle.
Course 2
9-2 Perimeter
Insert Lesson
Here
and Title
Circumference
Vocabulary
perimeter
circumference
Course 2
9-2 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
9-2 Perimeter and Circumference
Additional Example 1: Finding the Perimeter of a
Polygon
Find the perimeter.
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
9-2 Insert
Lesson
Here
Perimeter
and Title
Circumference
Check It Out: Example 1
Find the perimeter of the polygon.
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
9-2 Perimeter and Circumference
PERIMETER OF A RECTANGLE
The perimeter
P of a
rectangle is
the sum of
twice its
length l and
twice its
width w.
Course 2
P = 2l + 2w
w
l
9-2 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
Use the formula.
(2 · 18) + (2 ·14) Substitute for l and w.
Multiply.
36 + 28
Add.
64
The perimeter of the rectangle is 64 ft.
Course 2
9-2 Insert
Lesson
Here
Perimeter
and Title
Circumference
Check It Out: 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
9-2 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 Greek letter , called pi. Pi is
approximately equal to 3.14 or 22 . By solving the
7
C
equation =  for C, you get the formula for
d
circumference. the formula for circumference.
C = d, or C = 2r.
Course 2
9-2 Perimeter and Circumference
CIRCUMFERENCE OF A CIRCLE
The
circumference
C of a circle is
 times the
diameter d, or
2 times the
radius r.
Radius
C = d,
or
C = 2r
Diameter
Circumference
Course 2
9-2 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 .
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
9-2 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 .
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
9-2 Perimeter and Circumference
Check It Out: Example 3A
Find the circumference of the circle to the
nearest tenth. Use 3.14 for .
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 22.0 in.
Course 2
9-2 Perimeter and Circumference
Check It Out: Example 3B
Find the circumference of the circle to the
nearest tenth. Use 3.14 for .
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
9-2 Perimeter and Circumference
Helpful Hint
If the diameter or radius of a circle is a
22
multiple of 7, use for .
7
Course 2
9-2 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
9-2 Perimeter and Circumference
Check It Out: 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
9-2 Perimeter
Insert Lesson
and Title
Circumference
Here
Lesson Quiz
Find the perimeter.
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
Course 2
22
7
for . 66 ft