Learn to find the perimeter of a polygon and the circumference of a circle.
8-3 Perimeter Insert Lesson and Title Circumference Here perimeter circumference Vocabulary
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 Find the perimeter of the polygon. A. 4 in. 5 in. 4 in. 5 in. 4 in. P = 4 + 4 + 5 + 4 + 5 P = 22 Use the side lengths. Add. The perimeter of the pentagon is 22 in.
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.
8-3 Insert Perimeter Lesson and Title Circumference Here Try This: Example 1A Find the perimeter of the polygon. A. 5 in. 6 in. 4 in. 8 in. P = 5 + 6 + 8 + 4 P = 23 Use the side lengths. Add. The perimeter of the polygon is 23 in.
8-3 Insert Perimeter Lesson and Title Circumference Here Try This: Example 1B Find the perimeter of the polygon. B. 25 cm 20 cm 30 cm P = 25 + 20 + 30 P = 75 Use the side lengths. Add. The perimeter of the triangle is 75 cm.
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. l w
Additional Example 2: Using Properties of a Rectangle to Find Perimeter Find the perimeter of a rectangle. 18 ft 14 ft P = 2l + 2w P = (2 18) + (2 14) P = 36 + 28 P = 64 Use the formula. Substitute for l and w. Multiply. Add. The perimeter of the rectangle is 64 ft.
8-3 Insert Perimeter Lesson and Title Circumference Here Try This: Example 2 Find the perimeter of a rectangle. 16 ft 8 ft P = 2l + 2w P = (2 8) + (2 16) P = 16 + 32 P = 48 Use the formula. Substitute for l and w. Multiply. Add. The perimeter of the rectangle is 48 ft.
The distance around a circle is called circumference. For every circle, the ratio of circumference C to diameter d C 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 C = by d, you get d the formula for circumference, C = d or C = 2 r. Radius Diameter 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. 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.
Additional Example 3B: Finding the Circumference of a Circle Find the circumference of the circle to the nearest tenth. Use 3.14 for. B. 18 cm C = 2 r 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.
Try This: Example 3A Find the circumference of the circle to the nearest tenth. Use 3.14 for. A. 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.
Try This: Example 3B Find the circumference of the circle to the nearest tenth. Use 3.14 for. B. 11 cm C = 2 r 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.
Additional Example 4: Application The diameter of a circular pond is 42 m. What is its circumference? Use for. C = d 22 7 You know the diameter. C 22 7 42 Substitute 22 for and 42 for d. 7 C 22 7 42 Write 42 as a fraction. 1 C 22 7 42 6 Simplify. 1 1 C 132 Multiply. The circumference of the pond is about 132 m.
Try This: Example 4 The diameter of a circular spa is 14 m. What is its circumference? Use for. C = d 22 7 You know the diameter. C 22 7 14 Substitute 22 for and 14 for d. 7 C 22 7 14 Write 14 as a fraction. 1 C 22 7 14 2 Simplify. 1 1 C 44 Multiply. The circumference of the spa is about 44 m.
8-3 Perimeter Insert Lesson and Title Circumference Here Lesson Quiz Find the perimeter of each polygon. 1. 2. 8 m 12 m 10 m 9 m 6 m 45 m 10 in. 8 in. 36 in. 3. What is the circumference of a circle with a a radius of 8 inches? Use 3.14 for. 50.24 in. 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 22 7 for. 66 ft
Homework 8-3 Worksheet Study for fraction quiz Thursday