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8-3

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8-3

Perimeter and Circumference

Course 2

Warm Up

Problem of the Day

Lesson Presentation

8-3

Perimeter and Circumference

Course 2

Warm Up

Add or multiply.

1.8.2 + 5.6 + 8.2 + 5.6

2. 12.4 + 15.8 + 9.3

3. 4 · 8.5

4. 22 · 3.14

27.6

37.5

34

69.08

8-3

Perimeter and Circumference

Course 2

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

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)

8-3

Perimeter and Circumference

Course 2

Learn to find the perimeter of a polygon and the circumference of a circle.

8-3

Perimeter and Circumference

Course 2

Insert Lesson Title Here

Vocabulary

perimeter

circumference

8-3

Perimeter and Circumference

Course 2

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.

8-3

Perimeter and Circumference

Course 2

Additional Example 1A: Finding the Perimeter of a Polygon

Find the perimeter of the polygon.

A.

4 in.

4 in.

5 in.

5 in.

4 in.

Use the side lengths.

P = 4 + 4 + 5 + 4 + 5

Add.

P = 22

The perimeter of the pentagon is 22 in.

8-3

Perimeter and Circumference

Course 2

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.

8-3

Perimeter and Circumference

Course 2

Insert Lesson Title Here

Try This: Example 1A

Find the perimeter of the polygon.

5 in.

A.

4 in.

6 in.

8 in.

Use the side lengths.

P = 5 + 6 + 8 + 4

Add.

P = 23

The perimeter of the polygon is 23 in.

8-3

Perimeter and Circumference

Course 2

Insert Lesson Title Here

Try This: Example 1B

Find the perimeter of the polygon.

20 cm

B.

25 cm

30 cm

P = 25 + 20 + 30

Use the side lengths.

P = 75

Add.

The perimeter of the triangle is 75 cm.

8-3

Perimeter and Circumference

Course 2

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.

w

l

8-3

Perimeter and Circumference

Course 2

Additional Example 2: Using Properties of a Rectangle to Find Perimeter

Find the perimeter of a rectangle.

14 ft

18 ft

P = 2l+ 2w

Use the formula.

P = (2 ·18) + (2 ·14)

Substitute for l and w.

P = 36 + 28

Multiply.

P = 64

Add.

The perimeter of the rectangle is 64 ft.

8-3

Perimeter and Circumference

Course 2

Insert Lesson Title Here

Try This: Example 2

Find the perimeter of a rectangle.

16 ft

8 ft

P = 2l + 2w

Use the formula.

P = (2 · 8) + (2 · 16)

Substitute for l and w.

P = 16 + 32

Multiply.

P = 48

Add.

The perimeter of the rectangle is 48 ft.

8-3

Perimeter and Circumference

Course 2

The distance around a circle is

called circumference. For

every circle, the ratio of

circumference C to diameter d

is the same. This ratio,

Radius

C

d

, is

represented by the symbol ,

called pi. Pi is approximately

equal to 3.14 or . By

22

7

Diameter

multiplying both sides of the

equation

C

d

= by d, you get

Circumference

the formula for circumference,

C = d, or C = 2r.

8-3

Perimeter and Circumference

Course 2

Additional Example 3A: Finding the Circumference of a Circle

Find the circumference of the circle to the nearest tenth. Use 3.14 for .

A.

C = d

You know the diameter.

12 in.

C 3.14 · 12

Substitute for and d.

C 37.68

Multiply.

The circumference of the circle is about 37.7 in.

8-3

Perimeter and Circumference

Course 2

Additional Example 3B: Finding the Circumference of a Circle

Find the circumference of the circle to the nearest tenth. Use 3.14 for .

B.

C = 2r

You know the radius.

18 cm

C 2 · 3.14 · 18

Substitute for and r.

C 113.04

Multiply.

The circumference of the circle is about 113.0 cm.

8-3

Perimeter and Circumference

Course 2

Try This: Example 3A

Find the circumference of the circle to the nearest tenth. Use 3.14 for .

A.

C = d

You know the diameter.

7 in.

C 3.14 · 7

Substitute for and d.

C 21.98

Multiply.

The circumference of the circle is about 22 in.

8-3

Perimeter and Circumference

Course 2

Try This: Example 3B

Find the circumference of the circle to the nearest tenth. Use 3.14 for .

B.

C = 2r

You know the radius.

11 cm

C 2 · 3.14 · 11

Substitute for and r.

C 69.08

Multiply.

The circumference of the circle is about 69.1 cm.

8-3

Perimeter and Circumference

Course 2

Additional Example 4: Application

The diameter of a circular pond is 42 m. What is its circumference? Use

for .

22

7

You know the diameter.

C = d

22

7

22

7

· 42

Substitute

for and 42 for d.

C

22

7

42

1

Write 42 as a fraction.

C

·

6

22

7

42

1

·

Simplify.

C

1

C 132

Multiply.

The circumference of the pond is about 132 m.

8-3

Perimeter and Circumference

Course 2

Try This: Example 4

The diameter of a circular spa is 14 m. What is its circumference? Use

for .

22

7

You know the diameter.

C = d

22

7

22

7

· 14

Substitute

for and 14 for d.

C

22

7

14

1

Write 14 as a fraction.

C

·

2

22

7

14

1

·

Simplify.

C

1

C 44

Multiply.

The circumference of the spa is about 44 m.

8-3

Perimeter and Circumference

Course 2

Insert Lesson Title Here

Lesson Quiz

Find the perimeter of each polygon.

1.2.

3. What is the circumference of a circle with a

a radius of 8 inches? Use 3.14 for .

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

8 m

12 m

8 in.

10 m

45 m

36 in.

9 m

10 in.

6 m

50.24 in.

for .

66 ft

22

7