Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

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 69.08

out of the middle of each side. What is 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. (22 in. plus 8 in. for the eight 1 in. cuts)‏

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

Vocabulary perimeter circumference pi

Perimeter is the distance around a geometric figure Perimeter is the distance around a geometric figure. To find the perimeter P of a polygon, you can add the lengths of its sides.

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.

Check It Out: Example 1 Find the perimeter of the polygon. 20 cm 25 cm 30 cm P = 25 + 20 + 30 Use the side lengths. P = 75 Add. The perimeter of the triangle is 75 cm.

The perimeter of the rectangle is 64 ft. 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.

The perimeter of the rectangle is 48 ft. Check It Out: Example 2 Find the perimeter of a rectangle. 16 ft 8 ft P = 2l + 2w Use the formula. P = (2 · 16) + (2 · 8) Substitute for l and w. P = 32 + 16 Multiply. P = 48 Add. The perimeter of the rectangle is 48 ft.

equation =  for C, you get the formula for circumference. 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 , called pi. Pi is approximately equal to 3.14 or . By solving the 22 7 equation =  for C, you get the formula for circumference.

Example 1: Finding the Circumference of a Circle Find the circumference of the circle to the nearest tenth. Use 3.14 for . 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.

Example 2: Finding the Circumference of a Circle Find the circumference of the circle to the nearest tenth. Use 3.14 for . C = 2r 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.

C = d C  3.14 · 7 C  21.98 Check It Out: Example 3A Find the circumference of the circle to the nearest tenth. Use 3.14 for . 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 22.0 in.

Check It Out: Example 3B Find the circumference of the circle to the nearest tenth. Use 3.14 for . C = 2r 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.

If the diameter or radius of a circle is a multiple of 7, use for . Helpful Hint 22 7

for . Example 3: Application The diameter of a circular pond is 42 m. What is its circumference? Use for . 22 7 C = d You know the diameter. 22 7 22 7 C  · 42 Substitute for  and 42 for d. 22 7 42 1 C  · Write 42 as a fraction. 6 22 7 42 1 · C  Simplify. 1 C  132 Multiply. The circumference of the pond is about 132 m.

for . Check It Out: Example 3 The diameter of a circular spa is 14 m. What is its circumference? Use 22 7 for . C = d You know the diameter. 22 7 22 7 C  · 14 Substitute for  and 14 for d. 22 7 14 1 C  · Write 14 as a fraction. 2 22 7 14 1 · C  Simplify. 1 C  44 Multiply. The circumference of the spa is about 44 m.

Lesson Quiz for Student Response Systems Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 21

3. What is the circumference of a circle with a 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 . 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? 8 m 12 m 8 in. 10 m 45 m 36 in. 9 m 6 m 10 in. 50.24 in. Use for . 22 7 66 ft

Lesson Quiz for Student Response Systems 1. Identify the perimeter. A. 10 in. B. 15 in. C. 24 in. D. 48 in. 6 in. 6 in. 23

Lesson Quiz for Student Response Systems 2. Identify the perimeter. A. 52 m B. 82.5 m C. 165 m D. 330 m 18 m 8 m 24

Lesson Quiz for Student Response Systems 3. What is the circumference of a circle with a radius of 13 in.? Use 3.14 for . A. 40.82 in. B. 81.64 in. C. 265.33 in. D. 530.66 in. 25

Lesson Quiz for Student Response Systems 4. Jill plans to build a fence around her circular garden. About how many feet of fencing would be required if the garden has a diameter of 28 ft? A. 88 ft B. 66 ft C. 44 ft D. 22 ft 26