1. 1.4 Introduction to Perimeter, and Area in the coordinate plane.
Geometry
1.4 Introduction to Perimeter, and Area in the coordinate plane.

2. Geometry 1.4 Perimeter, Area
Topic/Objectives:
Find the perimeter and area of common plane figures.
To classify polygons.
To compare convex and concave polygons.
May 25, 2018
Geometry 1.4 Perimeter, Area

3. Geometry 1.4 Perimeter, Area
Square
Perimeter
P = 4s S S
Area
A = s2
May 25, 2018
Geometry 1.4 Perimeter, Area

4. Geometry 1.4 Perimeter, 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.
May 25, 2018
Geometry 1.4 Perimeter, Area

5. Geometry 1.4 Perimeter, Area
Rectangle
Perimeter
P = 2 l + 2w w
Area
A = lw l
May 25, 2018
Geometry 1.4 Perimeter, Area

6. Geometry 1.4 Perimeter, 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
May 25, 2018
Geometry 1.4 Perimeter, Area

7. Geometry 1.4 Perimeter, Area
Triangle
Perimeter
P = a + b + c c a h
Area b
May 25, 2018
Geometry 1.4 Perimeter, Area

8. Geometry 1.4 Perimeter, 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
May 25, 2018
Geometry 1.4 Perimeter, Area

9. Geometry 1.4 Perimeter, Area
Problem Solving Steps
Sketch
Label
Formulas
Reason
Conclusion
Check
May 25, 2018
Geometry 1.4 Perimeter, Area

10. Geometry 1.4 Perimeter, 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
May 25, 2018
Geometry 1.4 Perimeter, Area

11. Geometry 1.4 Perimeter, 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
May 25, 2018
Geometry 1.4 Perimeter, Area

12. Geometry 1.4 Perimeter, 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
May 25, 2018
Geometry 1.4 Perimeter, Area

13. 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
May 25, 2018
Geometry 1.4 Perimeter, Area

14. Geometry 1.4 Perimeter, Area
EX: Determine the perimeter of the polygon with the given vertices. A(-4,-1), B(1,4), C(4,1),D(-1, -4) B
Sketch
Label C A D
Formulas: Use distant formula to find each length.
May 25, 2018
Geometry 1.4 Perimeter, Area

15. Geometry 1.4 Perimeter, Area
EX: Find the area of the polygon with the given vertices. (-2,3),(3,-3),(-2,-3)
A = ½ bh 6
A = 15 5
May 25, 2018
Geometry 1.4 Perimeter, Area

16. Geometry 1.4 Perimeter, Area
Convex vs Concave
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Geometry 1.4 Perimeter, Area

17. Geometry 1.4 Perimeter, 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
May 25, 2018
Geometry 1.4 Perimeter, Area

18. Geometry 1.4 Perimeter, 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…
May 25, 2018
Geometry 1.4 Perimeter, Area

19. Geometry 1.4 Perimeter, 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
May 25, 2018
Geometry 1.4 Perimeter, Area

20. Geometry 1.4 Perimeter, 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.
May 25, 2018
Geometry 1.4 Perimeter, Area

21. Geometry 1.4 Perimeter, Area
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May 25, 2018
Geometry 1.4 Perimeter, Area