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8-3 Perimeter and Circumference Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation
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Warm Up Add or multiply. 1. 8.2 + 5.6 + 8.2 + 5.6 2. 12.4 + 15.8 + 9.3 3. 4 · 8.5 4. 22 · 3.14 27.6 37.5 34 Course 2 8-3 Perimeter and Circumference 69.08
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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 8-3 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)
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Learn to find the perimeter of a polygon and the circumference of a circle. Course 2 8-3 Perimeter and Circumference
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Vocabulary perimeter circumference Insert Lesson Title Here Course 2 8-3 Perimeter and Circumference
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Course 2 8-3 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.
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Find the perimeter of the polygon. Additional Example 1A: Finding the Perimeter of a Polygon Course 2 8-3 Perimeter and Circumference A. 4 in. 5 in. P = 4 + 4 + 5 + 4 + 5 Use the side lengths. P = 22 The perimeter of the pentagon is 22 in. Add.
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Find the perimeter of the polygon. Additional Example 1B: Finding the Perimeter of a Polygon Course 2 8-3 Perimeter and Circumference B. 25 cm 15 cm P = 25 + 25 + 15Use the side lengths. P = 65 The perimeter of the triangle is 65 cm. Add.
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Try This: Example 1A Insert Lesson Title Here Course 2 8-3 Perimeter and Circumference A. P = 5 + 6 + 8 + 4 Use the side lengths. P = 23 The perimeter of the polygon is 23 in. Add. Find the perimeter of the polygon. 6 in. 4 in. 5 in. 8 in.
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Try This: Example 1B Insert Lesson Title Here Course 2 8-3 Perimeter and Circumference B. 20 cm 25 cm 30 cm P = 25 + 20 + 30Use the side lengths. P = 75 The perimeter of the triangle is 75 cm. Add. Find the perimeter of the polygon.
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Course 2 8-3 Perimeter and Circumference You can find the perimeter of a rectangle by adding the length of its sides. Or, since opposite sides of a rectangle are equal in length, you can find the perimeter by using the formula P = 2l + 2w. w l
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Find the perimeter of a rectangle. Additional Example 2: Using Properties of a Rectangle to Find Perimeter Course 2 8-3 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.
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Try This: Example 2 Insert Lesson Title Here Course 2 8-3 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.
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Course 2 8-3 Perimeter and Circumference CdCd 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 symbol , called pi. Pi is approximately equal to 3.14 or. By 22 7 multiplying both sides of the equation CdCd = by d, you get the formula for circumference, C = d, or C = 2r. Radius Diameter Circumference
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Find the circumference of the circle to the nearest tenth. Use 3.14 for . Additional Example 3A: Finding the Circumference of a Circle 12 in. C = d C 3.14 · 12 C 37.68 You know the diameter. Substitute for and d. Multiply. The circumference of the circle is about 37.7 in. A. Course 2 8-3 Perimeter and Circumference
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Find the circumference of the circle to the nearest tenth. Use 3.14 for . Additional Example 3B: Finding the Circumference of a Circle 18 cm C = 2r C 2 · 3.14 · 18 C 113.04 You know the radius. Substitute for and r. Multiply. The circumference of the circle is about 113.0 cm. B. Course 2 8-3 Perimeter and Circumference
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Find the circumference of the circle to the nearest tenth. Use 3.14 for . Try This: Example 3A 7 in. C = d C 3.14 · 7 C 21.98 You know the diameter. Substitute for and d. Multiply. The circumference of the circle is about 22 in. A. Course 2 8-3 Perimeter and Circumference
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Find the circumference of the circle to the nearest tenth. Use 3.14 for . Try This: Example 3B 11 cm C = 2r C 2 · 3.14 · 11 C 69.08 You know the radius. Substitute for and r. Multiply. The circumference of the circle is about 69.1 cm. B. Course 2 8-3 Perimeter and Circumference
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The diameter of a circular pond is 42 m. What is its circumference? Use Additional Example 4: Application Course 2 8-3 Perimeter and Circumference 22 7 for . C = d You know the diameter. C 22 7 · 42Substitute 22 7 for 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.
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The diameter of a circular spa is 14 m. What is its circumference? Use Try This: Example 4 Course 2 8-3 Perimeter and Circumference 22 7 for . C = d You know the diameter. C 22 7 · 14Substitute 22 7 for 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.
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Lesson Quiz Find the perimeter of each polygon. 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? Use 36 in. 45 m Insert Lesson Title Here 50.24 in. 66 ft Course 2 8-3 Perimeter and Circumference 8 m 12 m 9 m 6 m 10 m 8 in. 10 in. 22 7 for .
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