Perimeter and Circumference
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This document is a mathematics lesson on calculating perimeter and circumference. It begins with examples of finding the perimeter of polygons by adding side lengths. It then explains that the perimeter of a rectangle can be calculated as 2 times the length plus 2 times the width. The lesson defines circumference as the distance around a circle and presents the formulas for calculating circumference using diameter or radius and pi. Examples are provided for calculating circumference of circles. The document provides guidance for when to use 22/7 as an approximation of pi.
Perimeter and Circumference
- 1. 9-2 Perimeter and Circumference Course 2 Warm UpWarm Up Problem of the DayProblem of the Day Lesson PresentationLesson Presentation
- 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 Course 2 9-2 Perimeter and Circumference 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 Course 2 9-2 Perimeter and Circumference 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. Learn to find the perimeter of a polygon and the circumference of a circle. Course 2 9-2 Perimeter and Circumference
- 5. Vocabulary perimeter circumference Insert Lesson Title Here Course 2 9-2 Perimeter and Circumference
- 6. Course 2 9-2 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.
- 7. Find the perimeter. Additional Example 1: Finding the Perimeter of a Polygon Course 2 9-2 Perimeter and Circumference 25 cm25 cm 15 cm P = 25 + 25 + 15 Use the side lengths. P = 65 The perimeter of the triangle is 65 cm. Add.
- 8. Check It Out: Example 1 Insert Lesson Title Here Course 2 9-2 Perimeter and Circumference 20 cm 25 cm 30 cm P = 25 + 20 + 30 Use the side lengths. P = 75 The perimeter of the triangle is 75 cm. Add. Find the perimeter of the polygon.
- 9. Course 2 9-2 Perimeter and Circumference The perimeter P of a rectangle is the sum of twice its length l and twice its width w. w l PERIMETER OF A RECTANGLE P = 2l + 2w
- 10. Find the perimeter of a rectangle. Additional Example 2: Using Properties of a Rectangle to Find Perimeter Course 2 9-2 Perimeter and Circumference 14 ft 18 ft P = 2l + 2w P = (2 · 18) + (2 ·14) P = 36 + 28 P = 64 The perimeter of the rectangle is 64 ft. Use the formula. Substitute for l and w. Multiply. Add.
- 11. Check It Out: Example 2 Insert Lesson Title Here Course 2 9-2 Perimeter and Circumference Find the perimeter of a rectangle. 16 ft 8 ft P = 2l + 2w P = (2 · 8) + (2 · 16) P = 16 + 32 P = 48 The perimeter of the rectangle is 48 ft. Use the formula. Substitute for l and w. Multiply. Add.
- 12. Course 2 9-2 Perimeter and Circumference C 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 π, called pi. Pi is approximately equal to 3.14 or . By solving the22 7 equation = π for C, you get the formula for circumference. the formula for circumference. C = πd, or C = 2πr. C d
- 13. Course 2 9-2 Perimeter and Circumference Radius Diameter Circumference C = πd, or C = 2πr CIRCUMFERENCE OF A CIRCLE The circumference C of a circle is π times the diameter d, or 2π times the radius r.
- 14. Find the circumference of the circle to the nearest tenth. Use 3.14 for π. Additional Example 3A: Finding the Circumference of a Circle 12 in. C = πd C ≈ 3.14 · 12 C ≈ 37.68 You know the diameter. Substitute for π and d. Multiply. The circumference of the circle is about 37.7 in. Course 2 9-2 Perimeter and Circumference
- 15. Find the circumference of the circle to the nearest tenth. Use 3.14 for π. Additional Example 3B: Finding the Circumference of a Circle 18 cm C = 2πr C ≈ 2 · 3.14 · 18 C ≈ 113.04 You know the radius. Substitute for π and r. Multiply. The circumference of the circle is about 113.0 cm. Course 2 9-2 Perimeter and Circumference
- 16. Find the circumference of the circle to the nearest tenth. Use 3.14 for π. Check It Out: Example 3A 7 in. C = πd C ≈ 3.14 · 7 C ≈ 21.98 You know the diameter. Substitute for π and d. Multiply. The circumference of the circle is about 22.0 in. Course 2 9-2 Perimeter and Circumference
- 17. Find the circumference of the circle to the nearest tenth. Use 3.14 for π. Check It Out: Example 3B 11 cm C = 2πr C ≈ 2 · 3.14 · 11 C ≈ 69.08 You know the radius. Substitute for π and r. Multiply. The circumference of the circle is about 69.1 cm. Course 2 9-2 Perimeter and Circumference
- 18. Course 2 9-2 Perimeter and Circumference If the diameter or radius of a circle is a multiple of 7, use for π. Helpful Hint 22 7
- 19. The diameter of a circular pond is 42 m. What is its circumference? Use Additional Example 4: Application Course 2 9-2 Perimeter and Circumference 22 7 for π. C = πd You know the diameter. C ≈ 22 7 · 42 Substitute 22 7 for π and 42 for d. C ≈ 22 7 · 42 1 C ≈ 22 7 · 42 1 6 1 C ≈ 132 The circumference of the pond is about 132 m. Write 42 as a fraction. Simplify. Multiply.
- 20. The diameter of a circular spa is 14 m. What is its circumference? Use Check It Out: Example 4 Course 2 9-2 Perimeter and Circumference 22 7 for π. C = πd You know the diameter. C ≈ 22 7 · 14 Substitute 22 7 for π and 14 for d. C ≈ 22 7 · 14 1 C ≈ 22 7 · 14 1 2 1 C ≈ 44 The circumference of the spa is about 44 m. Write 14 as a fraction. Simplify. Multiply.
- 21. 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 π. 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? 36 in.45 m Insert Lesson Title Here 50.24 in. 66 ft Course 2 9-2 Perimeter and Circumference 8 m 12 m 9 m 6 m 10 m 8 in. 10 in. 22 7 Use for π.