9 1 Perimeter and Circumference Warm Up Problem

9 -1 Perimeter and Circumference Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

9 -1 Perimeter and Circumference Warm Up Add or multiply. 1. 8. 2 + 5. 6 + 8. 2 + 5. 6 27. 6 2. 12. 4 + 15. 8 + 9. 3 37. 5 3. 22 · 3. 14 69. 08

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

9 -1 Perimeter and Circumference Learn to find the perimeter of a polygon and the circumference of a circle.

9 -1 Perimeter and Circumference Vocabulary perimeter circumference pi

9 -1 Perimeter and Circumference Perimeter is the distance around a geometric figure. To find the perimeter P of a polygon, you can add the lengths of its sides.

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

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

9 -1 Perimeter and Circumference

9 -1 Perimeter and Circumference Additional Example 2: Using Properties of a Rectangle to Find Perimeter Find the perimeter of a rectangle. 14 ft 18 ft P P = = 2 l + 2 w Use the formula. (2 · 18) + (2 · 14) Substitute for l and w. Multiply. 36 + 28 Add. 64 The perimeter of the rectangle is 64 ft.

9 -1 Perimeter and Circumference Check It Out: Example 2 Find the perimeter of a rectangle. 16 ft 8 ft P P = = 2 l + 2 w (2 · 16) + (2 · 8) 32 + 16 48 Use the formula. Substitute for l and w. Multiply. Add. The perimeter of the rectangle is 48 ft.

9 -1 Perimeter and Circumference The distance around a circle is called circumference. For every circle, the ratio of circumference C to diameter d is the same. This ratio, C , is d represented by the Greek letter , called pi. Pi is approximately equal to 3. 14 or 22. By solving the 7 C equation = for C, you get the formula for d circumference.

9 -1 Perimeter and Circumference

9 -1 Perimeter and Circumference Example 1: Finding the Circumference of a Circle Find the circumference of the circle to the nearest tenth. Use 3. 14 for . 12 in. C = d You know the diameter. C 3. 14 · 12 Substitute for and d. C 37. 68 Multiply. The circumference of the circle is about 37. 7 in.

9 -1 Perimeter and Circumference Example 2: Finding the Circumference of a Circle Find the circumference of the circle to the nearest tenth. Use 3. 14 for . 18 cm C = 2 r You know the radius. C 2 · 3. 14 · 18 Substitute for and r. C 113. 04 Multiply. The circumference of the circle is about 113. 0 cm.

9 -1 Perimeter and Circumference Check It Out: Example 3 A Find the circumference of the circle to the nearest tenth. Use 3. 14 for . 7 in. C = d C 3. 14 · 7 You know the diameter. C 21. 98 Multiply. Substitute for and d. The circumference of the circle is about 22. 0 in.

9 -1 Perimeter and Circumference Check It Out: Example 3 B Find the circumference of the circle to the nearest tenth. Use 3. 14 for . 11 cm C = 2 r You know the radius. C 2 · 3. 14 · 11 Substitute for and r. C 69. 08 Multiply. The circumference of the circle is about 69. 1 cm.

9 -1 Perimeter and Circumference Helpful Hint If the diameter or radius of a circle is a 22 multiple of 7, use for . 7

9 -1 Perimeter and Circumference Example 3: Application The diameter of a circular pond is 42 m. What is its circumference? Use 22 for . 7 C = d You know the diameter. C 22 · 42 7 1 22 · 42 6 C 7 1 1 C 132 Substitute 22 for and 42 for d. 7 Write 42 as a fraction. Simplify. Multiply. The circumference of the pond is about 132 m.

9 -1 Perimeter and Circumference Check It Out: Example 3 The diameter of a circular spa is 14 m. What is its circumference? Use 22 for . 7 C = d You know the diameter. C 22 · 14 7 1 22 · 14 2 C 7 1 1 C 44 Substitute 22 for and 14 for d. 7 Write 14 as a fraction. Simplify. Multiply. The circumference of the spa is about 44 m.

9 -1 Perimeter and Circumference Lesson Quizzes Standard Lesson Quiz for Student Response Systems

9 -1 Perimeter and Circumference Lesson Quiz Find the perimeter. 1. 8 m 12 m 10 m 6 m 9 m 2. 8 in. 45 m 36 in. 10 in. 3. What is the circumference of a circle with a a radius of 8 inches? Use 3. 14 for . 50. 24 in. 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 22 for . 66 ft 7

9 -1 Perimeter and Circumference Lesson Quiz for Student Response Systems 1. Identify the perimeter. A. 10 in. B. 15 in. C. 24 in. D. 48 in. 6 in.

9 -1 Perimeter and Circumference 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

9 -1 Perimeter and Circumference 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.

9 -1 Perimeter and Circumference 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