This document is a mathematics lesson on calculating perimeter and circumference. It begins with examples of finding the perimeter of polygons by adding side lengths. It then explains that the perimeter of a rectangle can be calculated as 2 times the length plus 2 times the width. The lesson defines circumference as the distance around a circle and presents the formulas for calculating circumference using diameter or radius and pi. Examples are provided for calculating circumference of circles. The document provides guidance for when to use 22/7 as an approximation of pi.

1. 9-2 Perimeter and Circumference
Course 2
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation

2. Warm Up
Add or multiply.
1. 8.2 + 5.6 + 8.2 + 5.6
2. 12.4 + 15.8 + 9.3
3. 22 · 3.14
27.6
37.5
Course 2
9-2 Perimeter and Circumference
69.08

3. Problem of the Day
A rectangular piece of sheet metal
measures 5 in. by 6 in. A rectangular
notch 1 in. deep and in. wide is cut
Course 2
9-2 Perimeter and Circumference
7
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)

4. Learn to find the perimeter of a polygon
and the circumference of a circle.
Course 2
9-2 Perimeter and Circumference

5. Vocabulary
perimeter
circumference
Insert Lesson Title Here
Course 2
9-2 Perimeter and Circumference

6. 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.

7. Find the perimeter.
Additional Example 1: Finding the Perimeter of a
Polygon
Course 2
9-2 Perimeter and Circumference
25 cm25 cm
15 cm
P = 25 + 25 + 15 Use the side lengths.
P = 65
The perimeter of the triangle is 65 cm.
Add.

8. Check It Out: Example 1
Insert Lesson Title Here
Course 2
9-2 Perimeter and Circumference
20 cm
25 cm
30 cm
P = 25 + 20 + 30 Use the side lengths.
P = 75
The perimeter of the triangle is 75 cm.
Add.
Find the perimeter of the polygon.

9. Course 2
9-2 Perimeter and Circumference
The perimeter
P of a
rectangle is
the sum of
twice its
length l and
twice its
width w.
w
l
PERIMETER OF A RECTANGLE
P = 2l + 2w

10. Find the perimeter of a rectangle.
Additional Example 2: Using Properties of a
Rectangle to Find Perimeter
Course 2
9-2 Perimeter and Circumference
14 ft
18 ft
P = 2l + 2w
P = (2 · 18) + (2 ·14)
P = 36 + 28
P = 64
The perimeter of the rectangle is 64 ft.
Use the formula.
Substitute for l and w.
Multiply.
Add.

11. Check It Out: Example 2
Insert Lesson Title Here
Course 2
9-2 Perimeter and Circumference
Find the perimeter of a rectangle.
16 ft
8 ft
P = 2l + 2w
P = (2 · 8) + (2 · 16)
P = 16 + 32
P = 48
The perimeter of the rectangle is 48 ft.
Use the formula.
Substitute for l and w.
Multiply.
Add.

12. Course 2
9-2 Perimeter and Circumference
C
d
The distance around a circle is called circumference.
For every circle, the ratio of circumference C to
diameter d is the same. This ratio, , is
represented by the Greek letter π, called pi. Pi is
approximately equal to 3.14 or . By solving the22
7
equation = π for C, you get the formula for
circumference. the formula for circumference.
C = πd, or C = 2πr.
C
d

13. Course 2
9-2 Perimeter and Circumference
Radius
Diameter
Circumference
C = πd, or
C =
2πr
CIRCUMFERENCE OF A CIRCLE
The
circumference
C of a circle is
π times the
diameter d, or
2π times the
radius r.

14. Find the circumference of the circle to the
nearest tenth. Use 3.14 for π.
Additional Example 3A: Finding the Circumference
of a Circle
12 in.
C = πd
C ≈ 3.14 · 12
C ≈ 37.68
You know the diameter.
Substitute for π and d.
Multiply.
The circumference of the circle is about 37.7 in.
Course 2
9-2 Perimeter and Circumference

15. Find the circumference of the circle to the
nearest tenth. Use 3.14 for π.
Additional Example 3B: Finding the Circumference
of a Circle
18 cm
C = 2πr
C ≈ 2 · 3.14 · 18
C ≈ 113.04
You know the radius.
Substitute for π and r.
Multiply.
The circumference of the circle is about 113.0 cm.
Course 2
9-2 Perimeter and Circumference

16. Find the circumference of the circle to the
nearest tenth. Use 3.14 for π.
Check It Out: Example 3A
7 in.
C = πd
C ≈ 3.14 · 7
C ≈ 21.98
You know the diameter.
Substitute for π and d.
Multiply.
The circumference of the circle is about 22.0 in.
Course 2
9-2 Perimeter and Circumference

17. Find the circumference of the circle to the
nearest tenth. Use 3.14 for π.
Check It Out: Example 3B
11 cm
C = 2πr
C ≈ 2 · 3.14 · 11
C ≈ 69.08
You know the radius.
Substitute for π and r.
Multiply.
The circumference of the circle is about 69.1 cm.
Course 2
9-2 Perimeter and Circumference

18. Course 2
9-2 Perimeter and Circumference
If the diameter or radius of a circle is a
multiple of 7, use for π.
Helpful Hint
22
7

19. The diameter of a circular pond is 42 m. What
is its circumference? Use
Additional Example 4: Application
Course 2
9-2 Perimeter and Circumference
22
7
for π.
C = πd You know the diameter.
C ≈ 22
7
· 42 Substitute 22
7
for π and 42 for d.
C ≈ 22
7
· 42
1
C ≈
22
7
· 42
1
6
1
C ≈ 132
The circumference of the pond is about 132 m.
Write 42 as a fraction.
Simplify.
Multiply.

20. The diameter of a circular spa is 14 m. What
is its circumference? Use
Check It Out: Example 4
Course 2
9-2 Perimeter and Circumference
22
7
for π.
C = πd You know the diameter.
C ≈ 22
7
· 14 Substitute 22
7
for π and 14 for d.
C ≈ 22
7
· 14
1
C ≈
22
7
· 14
1
2
1
C ≈ 44
The circumference of the spa is about 44 m.
Write 14 as a fraction.
Simplify.
Multiply.

21. Lesson Quiz
Find the perimeter.
1. 2.
3. What is the circumference of a circle with a
a radius of 8 inches? Use 3.14 for π.
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?
36 in.45 m
Insert Lesson Title Here
50.24 in.
66 ft
Course 2
9-2 Perimeter and Circumference
8 m
12 m
9 m
6 m
10 m
8 in.
10 in.
22
7
Use for π.