1. 3.2 Looking at Something Familiar in a New Way
Geometry
3.2 Looking at Something Familiar in a New Way

2. 3.2 Area and Perimeter of Triangles on the Coordinate Plane
Objectives
Determine the perimeter of triangles on the coordinate plane
Determine the area of triangles on the coordinate plane
Explore the effects that doubling the area has on the properties of a triangle

3. Problem 1 Determining the Area of a Triangle
Prior Knowledge: Area of a Parallelogram
𝐴𝑟𝑒𝑎 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙𝑜𝑔𝑟𝑎𝑚 =𝑏𝑎𝑠𝑒 𝑥 ℎ𝑒𝑖𝑔ℎ𝑡
Together #1

4. Problem 1 Determining the Area of a Triangle

5. Problem 1 Determining the Area of a Triangle
Formula for Area of a Triangle
𝐴𝑟𝑒𝑎 𝑇𝑟𝑖𝑎𝑛𝑔𝑙𝑒 = 1 2 𝑥 𝑏𝑎𝑠𝑒 𝑥 ℎ𝑒𝑖𝑔ℎ𝑡

6. Problem 1 Determining the Area of a Triangle
Collaborate 2-3 (8 Minutes)
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒= 𝑥 2 − 𝑥 𝑦 2 − 𝑦 1 2
𝐴𝑟𝑒𝑎 𝑇𝑟𝑖𝑎𝑛𝑔𝑙𝑒 = 1 2 𝑥 𝑏𝑎𝑠𝑒 𝑥 ℎ𝑒𝑖𝑔ℎ𝑡

7. Problem 1 Determining the Area of a Triangle

8. Problem 1 Determining the Area of a Triangle
Skip #4 and #5

9. Problem 1 Determining the Area of a Triangle
Together #6

10. Problem 2: Which Way is Up?
Wrap-Up
Explain how we can find a perimeter of a triangle
Describe the relationship of a base and a height
What is the formula for area of a triangle?
Collaborate 1-2 (Until the bell rings) Pg. 242
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒= 𝑥 2 − 𝑥 𝑦 2 − 𝑦 1 2

11. 3.2 Area and Perimeter of Triangles on the Coordinate Plane
Objectives
Determine the perimeter of triangles on the coordinate plane
Determine the area of triangles on the coordinate plane
Explore the effects that doubling the area has on the properties of a triangle

12. Problem 2: Which Way is Up?
Together 1-2 on Pg. 242 from Friday
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒= 𝑥 2 − 𝑥 𝑦 2 − 𝑦 1 2

14. Problem 2: Which Way is Up?
Together #2
The base and height must always be perpendicular when finding area
Does Point D have to be a Midpoint?

15. Problem 2: Which Way is Up?
(2, 5)
𝑦− 𝑦 1 =𝑚 𝑥− 𝑥 1
𝑦−5=−1 𝑥−2
𝑦=−𝑥+7

16. Problem 2: Which Way is Up?
Together #3 and #4

17. Problem 2: Which Way is Up?
(10, 9)
#4a Height (BD)
𝐵𝐷= 10− −3 2
𝐵𝐷=6 2 ≈8.485
#4b Area of the Triangle
Height = BD / Base = AC
𝐴= 1 2 𝑏ℎ 𝐴=
𝐴=24 𝑠𝑞𝑢𝑎𝑟𝑒 𝑢𝑛𝑖𝑡𝑠
(2, 5)
(4, 3)
(6, 1)

18. Talk the Talk Pg. 253 Collaborate What did he do wrong? (90 Seconds)
Emilio did not translate his point A’ back to the original picture.
The area is correct but A’ should be at (-5.5, 0.5) A’

19. Talk the Talk Pg. 253
In order to double the area of a triangle by manipulating the height, what must we do to the height?
𝐴= 1 2 𝑏ℎ
2𝐴= 1 2 𝑏ℎ 2
2𝐴= 1 2 𝑏(2ℎ)
If we want to double the area, we can double the height

20. Talk the Talk Pg. 253
In order to double the area of a triangle by manipulating the base, what must we do to the base?
𝐴= 1 2 𝑏ℎ
2𝐴= 1 2 𝑏ℎ 2
2𝐴= 𝑏 ℎ
If we want to double the area, we can double the base

21. Talk the Talk Pg. 253
What would happen to the area if we doubled the base AND we doubled the height?
𝐴= 1 2 (2𝑏)(2ℎ)
𝐴= 1 2 𝑏ℎ 4
The area would be multiplied by a total of 4

22. Talk the Talk Pg. 253 Base of Original Triangle 𝒃=𝟒 𝒖𝒏𝒊𝒕𝒔
Height of Original Triangle
ℎ=3 𝑢𝑛𝑖𝑡𝑠
Doubled Height
𝟐𝒉=𝟔 𝒖𝒏𝒊𝒕𝒔

23. Formative Assessment Formative Assessment Quiz 3.1-3.2
When finished, turn in onto round table
Work on assignment
Skills Practice 3.2 Pg
(3, 5, 8-10, 14-18)
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒= 𝑥 2 − 𝑥 𝑦 2 − 𝑦 1 2