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Goal 11.6

Goal 11.6. Circumference of a Circle. Things you should know about circles. A circle i s the set of all points in a plane that are the distance from a fixed point called the center . The distance from the center to any point on the circle is the radius .

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Goal 11.6

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  1. Goal 11.6 Circumference of a Circle

  2. Things you should know about circles. • A circleis the set of all points in a plane that are the distance from a fixed point called the center. • The distance from the center to any point on the circle is the radius. • The distance across the circle through the center is the diameter.

  3. a. l = 5 feet,w = 2 feet a. P = 2l + 2w The perimeter is 14 ft. ANSWER EXAMPLE 1 Finding Perimeter Find the perimeter of the rectangle or square with the given dimensions. SOLUTION = 2(5) + 2(2) = 10 + 4 = 14

  4. b. s = 3 centimeters b. P = 4s The perimeter is 12 cm. ANSWER EXAMPLE 1 Finding Perimeter Find the perimeter of the rectangle or square with the given dimensions. SOLUTION = 4(3) = 12

  5. a. l = 5 inches,w = 3 inches a. A = lw The area is 15 in. ANSWER 2 EXAMPLE 2 Finding Area Find the area of the rectangle or square with the given dimensions. SOLUTION = 5(3) = 15

  6. b. s = 10 feet b. A = s 2 2 = 10 . The area is 100 ft ANSWER 2 EXAMPLE 2 Finding Area Find the area of the rectangle or square with the given dimensions. SOLUTION = 100

  7. 2. 1. P = 16 m, A = 12 m2. P = 44 ft, A = 121 ft2. ANSWER ANSWER GUIDED PRACTICE for Examples 1 and 2 Find the perimeter and area of the rectangle or square.

  8. Find the perimeter and the area of a square with sides that are 30 yards long. Find the perimeter and the area of a rectangle that has a length of 6 inches and a width of 4 inches. 4. 3. P = 20 in.,A = 24 in.2 P = 120 yd,A = 900 yd2. ANSWER ANSWER GUIDED PRACTICE for Examples 1 and 2

  9. In a wheelchair slalom event, athletes weave around cones and race to the finish line. A diagram of the rectangular course is shown. Find the perimeter and the area of the course. EXAMPLE 3 Using Perimeter and Area Wheelchair Racing

  10. ANSWER The perimeter of the course is 92 m, and the area is 480 m2. EXAMPLE 3 Using Perimeter and Area SOLUTION A = lw P = 2l + 2w = 30(16) = 2(30) + 2(16) = 60 + 32 = 92 = 480

  11. What If? 5. In Example 3, suppose the wheelchair slalom course is 40 meters long and 24 meters wide. Find the perimeter and the area of the course. P = 128 m, A = 960 m2. ANSWER GUIDED PRACTICE for Example 3

  12. EXAMPLE 4 Standardized Test Practice

  13. Estimate the wall’s area using l = 16 feet and w = 10 feet. A = lengthwidth = 16(10) = 160 ft2 Calculate the window’s area: A = lengthwidth = 6(4) = 24 ft2. EXAMPLE 4 Standardized Test Practice SOLUTION STEP 1 STEP 2

  14. Divide the area by 20 to find the rolls needed: 136 20 = 6 R 16. ANSWER You need more than 6 rolls of wallpaper. So, you will need to buy 7 rolls of wallpaper. The correct answer is B. EXAMPLE 4 Standardized Test Practice SOLUTION STEP 3 Subtract to find the area you need to cover:160 – 24 = 136 ft2. STEP 4

  15. What If? 6. In Example 4, suppose the wall is 23 feet 11 inches long and 11 feet 10 inches high. How many rolls of wallpaper do you need? 14 rolls ANSWER GUIDED PRACTICE for Example 4

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