1. Introduction to Perimeter, Circumference and Area
Geometry
Introduction to Perimeter, Circumference and Area

2. Geometry 1.7 Perimeter, Circumference, Area
Goals:
Find the perimeter and area of common plane figures.
Use a general problem-solving plan.
April 23, 2017
Geometry 1.7 Perimeter, Circumference, Area

3. Geometry 1.7 Perimeter, Circumference, Area
Square
Perimeter
P = 4s S S
Area
A = s2
April 23, 2017
Geometry 1.7 Perimeter, Circumference, Area

4. Geometry 1.7 Perimeter, Circumference, Area
Square Problem
Each side of a square measures 2.5 m. Find its perimeter and its area.
P = 4(2.5) = 10 m
A = 2.52 = 6.25 m2
2.5 m
2.5 m
Area is a square measure.
April 23, 2017
Geometry 1.7 Perimeter, Circumference, Area

5. Geometry 1.7 Perimeter, Circumference, Area
Rectangle
Perimeter
P = 2 l + 2w w
Area
A = lw l
April 23, 2017
Geometry 1.7 Perimeter, Circumference, Area

6. Geometry 1.7 Perimeter, Circumference, Area
Rectangle Problem
Find the perimeter and the area.
4 ft
2.1 ft
P = 2(4) + 2(2.1) = = 12.2 ft
A = 4(2.1) = 8.4 ft2
April 23, 2017
Geometry 1.7 Perimeter, Circumference, Area

7. Geometry 1.7 Perimeter, Circumference, Area
Triangle
Perimeter
P = a + b + c c a h
Area b
April 23, 2017
Geometry 1.7 Perimeter, Circumference, Area

8. Geometry 1.7 Perimeter, Circumference, Area
Triangle Problem
Find the perimeter and the area.
8 in
3 in
2 in
10 in
P = = 21 in
A = ½ (10)(2) = 10 in2
April 23, 2017
Geometry 1.7 Perimeter, Circumference, Area

9. Geometry 1.7 Perimeter, Circumference, Area
Circle
Circumference
C = 2r r
Area
A = r2
April 23, 2017
Geometry 1.7 Perimeter, Circumference, Area

10. Geometry 1.7 Perimeter, Circumference, Area
Circle Problem
If the diameter is 8, find the circumference and the area.
r = 4 8
C = 2(4) = 8  25.13
(You could also use the formula C = d.)
A = (42) = 16  50.27
April 23, 2017
Geometry 1.7 Perimeter, Circumference, Area

11. Geometry 1.7 Perimeter, Circumference, Area
Problem Solving
Ask: What do I need to solve this problem? Draw a picture, if necessary, to help you determine this.
Label known and unknown facts.
Use labels and facts to choose related definitions, theorems, formulas, or other results you may need.
Reason logically to link the facts. Use a proof or other written argument.
Write a conclusion that answers the original problem. Check that your reasoning is correct.
April 23, 2017
Geometry 1.7 Perimeter, Circumference, Area

12. Geometry 1.7 Perimeter, Circumference, Area
Problem Solving Steps
Sketch
Label
Formulas
Reason
Conclusion
Check
April 23, 2017
Geometry 1.7 Perimeter, Circumference, Area

13. Geometry 1.7 Perimeter, Circumference, Area
Problem 1
A homeowner needs to fertilize a rectangular shaped yard that measures 20 ft by 30 ft. Each bag of fertilizer covers 150 square feet. How many bags of fertilizer will he need?
1. Sketch
2. label
30 ft.
A = ?
20 ft
April 23, 2017
Geometry 1.7 Perimeter, Circumference, Area

14. Geometry 1.7 Perimeter, Circumference, Area
Problem 1 Continued
A homeowner needs to fertilize a rectangular shaped yard that measures 20 ft by 30 ft. Each bag of fertilizer covers 150 square feet. How many bags of fertilizer will he need?
3. Formula: A = LW
a = 30(20) = 600 FT2
30 ft.
A = ?
20 ft
April 23, 2017
Geometry 1.7 Perimeter, Circumference, Area

15. Geometry 1.7 Perimeter, Circumference, Area
Problem 1 Continued
A homeowner needs to fertilize a rectangular shaped yard that measures 20 ft by 30 ft. Each bag of fertilizer covers 150 square feet. How many bags of fertilizer will he need?
4. Reason: Each bag covers 150 sq ft, and he needs to cover 600 sq ft. 600  150 = 4
30 ft.
20 ft
A = 600 FT2
April 23, 2017
Geometry 1.7 Perimeter, Circumference, Area

16. Problem 1 Conclusion
A homeowner needs to fertilize a rectangular shaped yard that measures 20 ft by 30 ft. Each bag of fertilizer covers 150 square feet. How many bags of fertilizer will he need?
5. Conclusion: He needs to buy 4 bags of fertilizer.
30 ft.
6. Check: 4  150 = 600
20 ft
A = 600 FT2
April 23, 2017
Geometry 1.7 Perimeter, Circumference, Area

17. Geometry 1.7 Perimeter, Circumference, Area
Problem 2
You are making a mat for a picture. The picture is 8 inches wide and 10 inches high. The mat is to have a width of 2 inches. What is the area of the mat? 8 2 10 2
April 23, 2017
Geometry 1.7 Perimeter, Circumference, Area

18. Geometry 1.7 Perimeter, Circumference, Area
Problem 2 Continued
You are making a mat for a picture. The picture is 8 inches wide and 10 inches high. The mat is to have a width of 2 inches. What is the area of the mat?
Think: Larger mat, cut away the inside…
April 23, 2017
Geometry 1.7 Perimeter, Circumference, Area

19. Geometry 1.7 Perimeter, Circumference, Area
Problem 2 Continued
You are making a mat for a picture. The picture is 8 inches wide and 10 inches high. The mat is to have a width of 2 inches. What is the area of the mat?
We need to know the area of the outer rectangle. 12
Left over Area =
168 – 80 = 88 in2
Outer Area =
12  14 = 168 8 14 2 10
Inner Area =
8  10 = 80 2
April 23, 2017
Geometry 1.7 Perimeter, Circumference, Area

20. Geometry 1.7 Perimeter, Circumference, Area
Problem 3: You do it.
You are making a triangular shaped window. The height of the window is 18 inches and the area will be 297 square inches. What will the length of the base of the window be? 18 b
The base will be 33 in.
April 23, 2017
Geometry 1.7 Perimeter, Circumference, Area

21. Geometry 1.7 Perimeter, Circumference, Area
Homework
April 23, 2017
Geometry 1.7 Perimeter, Circumference, Area