8-3 Perimeter and Circumference

Course 2

Warm UpProblem of the DayLesson Presentation

Warm UpAdd or multiply.

1. 8.2 + 5.6 + 8.2 + 5.6 2. 12.4 + 15.8 + 9.33. 4 · 8.54. 22 · 3.14

27.637.534

Course 2

8-3 Perimeter and Circumference

69.08

Problem of the DayA rectangular piece of sheet metal measures 5 in. by 6 in. A rectangular notch 1 in. deep and in. wide is cut

Course 2

8-3 Perimeter and Circumference

764out 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)

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

Course 2

8-3 Perimeter and Circumference

Vocabularyperimetercircumference

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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 = 22The 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 cmP = 25 + 25 + 15 Use the side lengths.

P = 65The 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 = 23The 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 cm30 cm

P = 25 + 20 + 30 Use the side lengths.

P = 75The 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 ftP = 2l + 2wP = (2 ·18) + (2 ·14)P = 36 + 28P = 64The 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 + 32P = 48The 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, , isrepresented by the symbol , called pi. Pi is approximatelyequal to 3.14 or . By22

7multiplying 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 = dC 3.14 · 12C 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 = 2rC 2 · 3.14 · 18C 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 = dC 3.14 · 7C 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 = 2rC 2 · 3.14 · 11C 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 · 42

1C

227 · 42

16

1C 132The 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 · 14

1C

227 · 14

12

1C 44The circumference of the spa is about 44 m.

Write 14 as a fraction.

Simplify.

Multiply.

Lesson QuizFind 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

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 m 8 in.

10 in.

227

for .