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8-3

8-3. Perimeter and Circumference. Course 2. Warm Up. Problem of the Day. Lesson Presentation. 8-3. Perimeter and Circumference. Course 2. Warm Up Convert 1. 6.78 kilograms = ________grams 2. 2345 cm = _________meters 3. 27,360 inchs + 8280 ft = _______miles. 8-3.

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  1. 8-3 Perimeter and Circumference Course 2 Warm Up Problem of the Day Lesson Presentation

  2. 8-3 Perimeter and Circumference Course 2 Warm Up Convert 1. 6.78 kilograms = ________grams 2. 2345 cm = _________meters 3. 27,360 inchs + 8280 ft = _______miles

  3. 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)

  4. 8-3 Perimeter and Circumference Course 2 Learn to find the perimeter of a polygon and the circumference of a circle.

  5. 8-3 Perimeter and Circumference Course 2 Insert Lesson Title Here Vocabulary perimeter circumference

  6. 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.

  7. 8-3 Perimeter and Circumference Course 2 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.

  8. 8-3 Perimeter and Circumference Course 2 Insert Lesson Title Here 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.

  9. 8-3 Perimeter and Circumference Course 2 The perimeter P of a rectangle is the sum of twice its length l and twice its width w. w l

  10. 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.

  11. 8-3 Perimeter and Circumference Course 2 Insert Lesson Title Here Check It Out: 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.

  12. 8-3 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, , is C d represented by the Greek letter , called pi. Pi is approximately equal to 3.14 or . By solving the 22 7 C d equation = for C, you getthe formula for circumference. the formula for circumference. C = d, or C = 2r. Course 2

  13. 8-3 Perimeter and Circumference Course 2 Radius C = d, or C = 2r Diameter Circumference

  14. 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 . 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.

  15. 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 . 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.

  16. 8-3 Perimeter and Circumference Course 2 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.

  17. 8-3 Perimeter and Circumference Course 2 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.

  18. 8-3 Perimeter and Circumference Helpful Hint If the diameter or radius of a circle is a multiple of 7, use for p. 22 7 Course 2

  19. 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.

  20. 8-3 Perimeter and Circumference Course 2 Check It Out: 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.

  21. 8-3 Perimeter and Circumference Course 2 Insert Lesson Title Here 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 10 in. 6 m 50.24 in. 22 7 Use for . 66 ft

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