Learn to find the perimeter of a polygon

and the circumference of a circle.

Course 2

8-3 Perimeter and Circumference

Vocabulary

perimeter

circumference

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Course 2

8-3 Perimeter and 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.

Find the perimeter of the polygon.

Additional Example 1A: Finding the Perimeter of a

Polygon

Course 2

8-3 Perimeter and Circumference

A. 4 in.4 in.

4 in.

5 in.5 in.

P = 4 + 4 + 5 + 4 + 5 Use the side lengths.

P = 22

The perimeter of the pentagon is 22 in.

Add.

Find the perimeter of the polygon.

Additional Example 1B: Finding the Perimeter of a

Polygon

Course 2

8-3 Perimeter and Circumference

B.25 cm25 cm

15 cm

P = 25 + 25 + 15 Use the side lengths.

P = 65

The perimeter of the triangle is 65 cm.

Add.

Try This: Example 1A

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Course 2

8-3 Perimeter and Circumference

A.

P = 5 + 6 + 8 + 4 Use the side lengths.

P = 23

The perimeter of the polygon is 23 in.

Add.

Find the perimeter of the polygon.

6 in. 4 in.

5 in.

8 in.

Try This: Example 1B

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Course 2

8-3 Perimeter and Circumference

B. 20 cm25 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.

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.

w

l

Find the perimeter of a rectangle.

Additional Example 2: Using Properties of a

Rectangle to Find Perimeter

Course 2

8-3 Perimeter and Circumference

14 ft

18 ft

P = 2l + 2wP = (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.

Try This: Example 2

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Course 2

8-3 Perimeter and Circumference

Find the perimeter of a rectangle.

16 ft

8 ft

P = 2l + 2wP = (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.

Course 2

8-3 Perimeter and Circumference

Cd

The distance around a circle iscalled circumference. For every circle, the ratio of circumference C to diameter dis the same. This ratio, , is

represented by the symbol , called pi. Pi is approximately

equal to 3.14 or . By227

multiplying both sides of the equation C

d= by d, you get

the formula for circumference,C = d or C = 2r.

Radius

Diameter

Circumference

Find the circumference of the circle to the

nearest tenth. Use 3.14 for .

Additional Example 3A: Finding the Circumference

of a Circle

12 in.C = d

C 3.14 · 12

C 37.68

You know the diameter.

Substitute for and d.

Multiply.

The circumference of the circle is about 37.7 in.

A.

Course 2

8-3 Perimeter and Circumference

Find the circumference of the circle to the

nearest tenth. Use 3.14 for .

Additional Example 3B: Finding the Circumference

of a Circle

18 cmC = 2r

C 2 · 3.14 · 18

C 113.04

You know the radius.

Substitute for and r.

Multiply.

The circumference of the circle is about 113.0 cm.

B.

Course 2

8-3 Perimeter and Circumference

Find the circumference of the circle to the

nearest tenth. Use 3.14 for .

Try This: Example 3A

7 in.C = d

C 3.14 · 7

C 21.98

You know the diameter.

Substitute for and d.

Multiply.

The circumference of the circle is about 22 in.

A.

Course 2

8-3 Perimeter and Circumference

Find the circumference of the circle to the

nearest tenth. Use 3.14 for .

Try This: Example 3B

11 cmC = 2r

C 2 · 3.14 · 11

C 69.08

You know the radius.

Substitute for and r.

Multiply.

The circumference of the circle is about 69.1 cm.

B.

Course 2

8-3 Perimeter and Circumference

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

Additional Example 4: Application

Course 2

8-3 Perimeter and Circumference

227

for .

C = d You know the diameter.

C 227

· 42 Substitute 227

for and 42 for d.

C 227

· 421

C 227

· 421

6

1C 132

The circumference of the pond is about 132 m.

Write 42 as a fraction.

Simplify.

Multiply.

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

Try This: Example 4

Course 2

8-3 Perimeter and Circumference

227

for .

C = d You know the diameter.

C 227

· 14 Substitute 227

for and 14 for d.

C 227

· 141

C 227

· 141

2

1C 44

The circumference of the spa is about 44 m.

Write 14 as a fraction.

Simplify.

Multiply.

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 edgeof a circular swimming pool with a diameter of 21 ft, how many feet of railing will be needed?Use

36 in.45 m

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50.24 in.

66 ft

Course 2

8-3 Perimeter and Circumference

8 m12 m

9 m6 m

10 m8 in.

10 in.

227

for .

Homework8-3 Worksheet

Study for fraction quiz Thursday