1. Perimeter and Circumference
Lesson 3.4
Perimeter and Circumference pp

2. Objectives:
1. To define and calculate perimeter
and circumference.
2. To identify a formula for the perimeter of a regular polygon.
3. To identify a formula for the
circumference of a circle.

3. Definition Perimeter is the distance around a closed curve. A B C 8 410

4. Theorem 3.2
The perimeter of a regular n-gon with sides of length s is n • s. M L K J N 9

5. Definition
Circumference is the distance around a circle.

6. Given the diameter (d) of a circle, the circumference (C) is
C = πd.
Since the diameter is twice the radius (r),
C = 2πr.

7. Find the perimeter of the following figure.2 3 4

8. Find the perimeter of the following figure.6

9. Find the perimeter of the following figure.3 7

10. Find the circumference of the following figure.4

11. The perimeter of a square is 64 cm. What is the length of each side?

12. A triangle ABC has a perimeter of 33 m
A triangle ABC has a perimeter of 33 m. The lengths of the sides are in a ratio of 5:4:2. What are the side lengths of ABC?

13. Homework pp

14. ►A. Exercises
Find the perimeter of each polygon.
9. A quadrilateral with sides 3, 5, 15, and 8.

15. ►B. Exercises
Find the perimeter of each polygon.
11. A regular quadrilateral ABCD has a perimeter of 72 meters. What is the length of each side?

16. ►B. Exercises
Find the perimeter of each polygon.
13. The perimeter of a triangle is inches. Side a is twice as long as side b and c is 2 inches longer than side a. Find the length of each side.

17. ►B. Exercises
Complete the following table of circle measurements.
d r c c
 terms decimal
  12
12
37.68 9
4.5 9 6 6
18.84

18. ►C. Exercises
Find the answer to the nearest tenth.
21. How far does a bicycle travel in one revolution of its 26-inch tire?

19. ►C. Exercises
Find the answer to the nearest tenth.
23. The hands of a clock vary in length. If the hour hand in 4 inches long, the minute hand 6 inches long, and the second hand 7 inches long, how long does the point of each hand travel in one day?

20. ►C. Exercises
Find the answer to the nearest tenth.
25. A circular track has a radius of feet. What is the circumference of the track in yards?

21. ■ Cumulative Review
26. What are the three criteria for an ideal postulate system?

22. ■ Cumulative Review
27. What did Kurt Gödel prove about these three criteria in 1936?

23. ■ Cumulative Review
28. What criterion is the most important?

24. ■ Cumulative Review
29. Find the coordinate of N if LM = 5, MN = 3, M is between L and N, and the coordinate of L is -7.

25. ■ Cumulative Review
30. If x  7, then what can you conclude about x? Explain.