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**Perimeter and Circumference**

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

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**Perimeter and Circumference**

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

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**Perimeter and Circumference**

Course 2 8-3 Perimeter and Circumference 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)

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**Perimeter and Circumference**

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

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**Insert Lesson Title Here**

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

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**Perimeter and Circumference**

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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**Additional Example 1: Finding the Perimeter of a Polygon**

Course 2 8-3 Perimeter and Circumference Additional Example 1: Finding the Perimeter of a Polygon Find the perimeter. 25 cm 25 cm 15 cm P = Use the side lengths. P = 65 Add. The perimeter of the triangle is 65 cm.

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**Insert Lesson Title Here**

Course 2 8-3 Perimeter and Circumference Insert Lesson Title Here Check It Out: Example 1 Find the perimeter of the polygon. 20 cm 25 cm 30 cm P = Use the side lengths. P = 75 Add. The perimeter of the triangle is 75 cm.

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**PERIMETER OF A RECTANGLE**

Course 2 8-3 Perimeter and Circumference PERIMETER OF A RECTANGLE P = 2l + 2w The perimeter P of a rectangle is the sum of twice its length l and twice its width w. w l

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**Perimeter and Circumference**

Course 2 8-3 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 = 2l + 2w Use the formula. P = (2 · 18) + (2 ·14) Substitute for l and w. P = Multiply. P = 64 Add. The perimeter of the rectangle is 64 ft.

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**Insert Lesson Title Here**

Course 2 8-3 Perimeter and Circumference 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 = Multiply. P = 48 Add. The perimeter of the rectangle is 48 ft.

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**Perimeter and Circumference**

Course 2 8-3 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 , called pi. Pi is approximately equal to 3.14 or By solving the 22 7 equation = for C, you get the formula for circumference. the formula for circumference. C = d, or C = 2r.

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**CIRCUMFERENCE OF A CIRCLE**

Course 2 8-3 Perimeter and Circumference CIRCUMFERENCE OF A CIRCLE The circumference C of a circle is times the diameter d, or 2 times the radius r. Radius C = d, or C = 2r Diameter Circumference

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**Additional Example 3A: Finding the Circumference of a Circle**

Course 2 8-3 Perimeter and Circumference 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.

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**Additional Example 3B: Finding the Circumference of a Circle**

Course 2 8-3 Perimeter and Circumference Additional Example 3B: Finding the Circumference of a Circle Find the circumference of the circle to the nearest tenth. Use 3.14 for . C = 2r You know the radius. 18 cm C 2 · 3.14 · 18 Substitute for and r. C Multiply. The circumference of the circle is about cm.

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**Perimeter and Circumference**

Course 2 8-3 Perimeter and Circumference 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.

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**Perimeter and Circumference**

Course 2 8-3 Perimeter and Circumference Check It Out: Example 3B Find the circumference of the circle to the nearest tenth. Use 3.14 for . C = 2r 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.

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**Perimeter and Circumference**

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

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**Additional Example 4: Application**

Course 2 8-3 Perimeter and Circumference Additional Example 4: Application The diameter of a circular pond is 42 m. What is its circumference? Use for . 22 7 C = d You know the diameter. 22 7 22 7 C · 42 Substitute for and 42 for d. 22 7 42 1 C Write 42 as a fraction. 6 22 7 42 1 C Simplify. 1 C 132 Multiply. The circumference of the pond is about 132 m.

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**Perimeter and Circumference**

Course 2 8-3 Perimeter and Circumference Check It Out: Example 4 The diameter of a circular spa is 14 m. What is its circumference? Use 22 7 for . C = d You know the diameter. 22 7 22 7 C · 14 Substitute for and 14 for d. 22 7 14 1 C Write 14 as a fraction. 2 22 7 14 1 C Simplify. 1 C 44 Multiply. The circumference of the spa is about 44 m.

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**Perimeter and Circumference Insert Lesson Title Here**

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

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