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Perimeter and Circumference Lesson

This lesson covers finding the perimeter of polygons and the circumference of circles using examples and formulas. It also includes practice problems.

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Perimeter and Circumference Lesson

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  1. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

  2. 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

  3. 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)‏

  4. I can find the perimeter of a polygon and the circumference of a circle.

  5. Vocabulary perimeter circumference pi

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

  7. 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. 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. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. I can find the perimeter of a polygon and 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. 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.

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

  17. I can find the perimeter of a polygon and the circumference of a circle. 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.

  18. 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.

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