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

Perimeter and Circumference Course 2 8-3 Perimeter and Circumference 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 69.08

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)

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

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

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.

Additional Example 1A: Finding the Perimeter of a Polygon Course 2 8-3 Perimeter and Circumference Additional Example 1A: Finding the Perimeter of a Polygon Find the perimeter of the polygon. A. 4 in. 4 in. 5 in. 5 in. 4 in. P = 4 + 4 + 5 + 4 + 5 Use the side lengths. P = 22 Add. The perimeter of the pentagon is 22 in.

Additional Example 1B: Finding the Perimeter of a Polygon Course 2 8-3 Perimeter and Circumference Additional Example 1B: Finding the Perimeter of a Polygon Find the perimeter of the polygon. B. 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.

Insert Lesson Title Here Course 2 8-3 Perimeter and Circumference Insert Lesson Title Here Try This: Example 1A Find the perimeter of the polygon. 5 in. A. 6 in. 4 in. 8 in. P = 5 + 6 + 8 + 4 Use the side lengths. P = 23 Add. The perimeter of the polygon is 23 in.

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

Perimeter and Circumference 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

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 = 36 + 28 Multiply. P = 64 Add. The perimeter of the rectangle is 64 ft.

Insert Lesson Title Here Course 2 8-3 Perimeter and Circumference Insert Lesson Title Here Try This: 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 = 16 + 32 Multiply. P = 48 Add. The perimeter of the rectangle is 48 ft.

Perimeter and Circumference Course 2 8-3 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 d Radius , is represented by the symbol , called pi. Pi is approximately equal to 3.14 or . By 22 7 Diameter multiplying both sides of the equation C d =  by d, you get Circumference the formula for circumference, C = d, or C = 2r.

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 . A. 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.

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 . B. 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.

Perimeter and Circumference Course 2 8-3 Perimeter and Circumference Try This: Example 3A Find the circumference of the circle to the nearest tenth. Use 3.14 for . A. 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 in.

Perimeter and Circumference Course 2 8-3 Perimeter and Circumference Try This: Example 3B Find the circumference of the circle to the nearest tenth. Use 3.14 for . B. 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.

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 22 7 for . 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.

Perimeter and Circumference Course 2 8-3 Perimeter and Circumference Try This: 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.

Perimeter and Circumference Insert Lesson Title Here Course 2 8-3 Perimeter and Circumference Insert Lesson Title Here 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 8 m 12 m 8 in. 10 m 45 m 36 in. 9 m 6 m 10 in. 50.24 in. for . 66 ft 22 7