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9-1 Perimeter and Circumference Warm Up Problem of the Day Lesson Presentation Lesson Quizzes 9-1 Perimeter and Circumference Warm Up Add or multiply. 1. 8.2 + 5.6 + 8.2 + 5.6 27.6 2. 12.4 + 15.8 + 9.3 37.5 3. 22 · 3.14 69.08 9-1 Perimeter and Circumference Problem of the Day A rectangular piece of sheet metal measures 5 in. by 6 in. A rectangular 7 notch 1 in. deep and in. wide is cut 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) 9-1 Perimeter and Circumference I can find the perimeter of a polygon and the circumference of a circle. 9-1 Perimeter and Circumference Vocabulary perimeter circumference pi 9-1 Perimeter and Circumference Perimeter is the distance around a geometric figure. To find the perimeter P of a polygon, you can add the lengths of its sides. 9-1 Perimeter and Circumference 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. 9-1 Perimeter and Circumference Check It Out: Example 1 Find the perimeter of the polygon. 25 cm 20 cm 30 cm P = 25 + 20 + 30 Use the side lengths. P = 75 Add. The perimeter of the triangle is 75 cm. 9-1 Perimeter and Circumference 9-1 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 P P P = = = = 2l + 2w Use the formula. (2 · 18) + (2 ·14) Substitute for l and w. Multiply. 36 + 28 Add. 64 The perimeter of the rectangle is 64 ft. 9-1 Perimeter and Circumference Check It Out: Example 2 Find the perimeter of a rectangle. 16 ft 8 ft P P P P = = = = 2l + 2w (2 · 16) + (2 · 8) 32 + 16 48 Use the formula. Substitute for l and w. Multiply. Add. The perimeter of the rectangle is 48 ft. 9-1 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, C , is d represented by the Greek letter , called pi. Pi is approximately equal to 3.14 or 22 . By solving the 7 C equation = for C, you get the formula for d circumference. 9-1 Perimeter and Circumference 9-1 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 . 12 in. C = d You know the diameter. C 3.14 · 12 Substitute for and d. C 37.68 Multiply. The circumference of the circle is about 37.7 in. 9-1 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 . 18 cm C = 2r You know the radius. C 2 · 3.14 · 18 Substitute for and r. C 113.04 Multiply. The circumference of the circle is about 113.0 cm. 9-1 Perimeter and Circumference Check It Out: Example 3A Find the circumference of the circle to the nearest tenth. Use 3.14 for . 7 in. C = d You know the diameter. C 3.14 · 7 Substitute for and d. C 21.98 Multiply. The circumference of the circle is about 22.0 in. 9-1 Perimeter and Circumference 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 . 11 cm C = 2r You know the radius. C 2 · 3.14 · 11 Substitute for and r. C 69.08 Multiply. The circumference of the circle is about 69.1 cm. 9-1 Perimeter and Circumference Helpful Hint If the diameter or radius of a circle is a 22 multiple of 7, use for . 7 9-1 Perimeter and Circumference 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 22 for . 7 C = d You know the diameter. C 22 · 42 7 C 22 · 42 7 1 22 · 42 6 C 7 1 1 C 132 Substitute 22 for and 42 for d. 7 Write 42 as a fraction. Simplify. Multiply. The circumference of the pond is about 132 m. 9-1 Perimeter and Circumference Check It Out: Example 4 The diameter of a circular spa is 14 m. What is its circumference? Use 22 for . 7 C = d You know the diameter. C 22 · 14 7 C 22 · 14 7 1 22 · 14 2 C 7 1 1 C 44 Substitute 22 for and 14 for d. 7 Write 14 as a fraction. Simplify. Multiply. The circumference of the spa is about 44 m.