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MODULE 3 LESSON 2 PROPERTIES OF AREA

OPENING EXERCISE Complete the Exploratory Challenge 1, parts a and b, in your workbook.

DISCUSSION Consider Exploratory Challenge 2.  Explain how we can calculate the area of the entire figure. The on the ends are congruent and their areas are easily 1 found by × 푏푎푠푒 × ℎ푒𝑖푔ℎ푡. 2 The section in the middle is a . Its area is found by 푙푒푛푔푡ℎ × 푤𝑖푑푡ℎ. Once the separate areas are found, they are added together for the total area.  Calculate the area. 1 퐴푟푒푎 표푓 푡푤표 푡푟𝑖푎푛푔푙푒푠 = 2 ( ) (3)(3) = 9 2 퐴푟푒푎 표푓 푡ℎ푒 푟푒푐푡푎푛푔푙푒 = (3)(7) = 21 푇표푡푎푙 퐴푟푒푎 = 9 + 21 = 30

Consider Exploratory Challenge 3. 퐴퐷 = 4, 퐷퐶 = 3, and 퐶퐹 = 2.  Explain how we can calculate the area of the entire figure. Calculate the area of ∆퐴퐵퐶 and ∆퐷퐸퐹. Since ∆퐷퐺퐶 represents the overlapping area shared by ∆퐴퐵퐶 and ∆퐷퐸퐹, its area must be subtracted from the sum of the areas of ∆퐴퐵퐶 and ∆퐷퐸퐹. This avoids “counting twice.”

MOD3 L2 1  Calculate the area of the figure ABGEF. 1 퐴푟푒푎 표푓∆퐴퐵퐶 = ( ) (7)(4) = 14 2 1 퐴푟푒푎 표푓∆퐷퐸퐹 = ( ) (5)(2) = 5 2 1 퐴푟푒푎 표푓∆퐷퐺퐶 = ( ) (3)(0.9) = 1.35 2 퐴푟푒푎 표푓퐴퐵퐺퐸퐹 = 14 + 5 − 1.35 = 17.65

Consider Exploratory Challenge 4.  Explain how we can calculate the area of the entire figure. Subtract the area of the from the area of the rectangle to find the area of the shaded region.  Calculate the area. 퐴푟푒푎 표푓푅푒푐푡푎푛푔푙푒 = (12)(21.4) = 259.2 1 퐴푟푒푎 표푓 푇푟𝑖푎푛푔푙푒 = ( ) (9.6)(7.2) = 34.56 2 퐴푟푒푎 표푓푆ℎ푎푑푒푑 푅푒푔𝑖표푛 = 259.2 − 34.56 = 224.64

PROPERTITES OF AREA 1. The area of a set in the is a number, greater than or equal to zero, that the of the set and not the . 2. The area of a rectangle is given by the 푙푒푛푔푡ℎ × 푤𝑖푑푡ℎ. The area of a triangle is given 1 by the formula × 푏푎푠푒 × ℎ푒𝑖푔ℎ푡. A polygonal region is the union of finitely many non- 2 overlapping triangular regions and has area the sum of the areas of the . 3. Congruent regions have the same area. (Example: Challenge 1 and 2) 4. The area of the union of two regions is the sum of the areas minus the area of intersection. (Example: Challenge 3) 5. The area of the difference of two regions where one is contained in the other is the difference of the areas. (Example: Challenge 4)

MOD3 L2 2 ON YOUR OWN Wooden pieces in the following shapes and are nailed together to create a sign in the shape of an arrow. The pieces are nailed together so that the rectangular piece overlaps with the triangular piece by 4 . What is the area of the region in the shape of the arrow?

퐴푟푒푎 (퐴푟푟표푤) = 퐴푟푒푎(푅푒푐푡푎푛푔푙푒) + 퐴푟푒푎(푇푟𝑖푎푛푔푙푒) − 퐴푟푒푎 (푂푣푒푟푙푎푝)

퐴푟푒푎(푅푒푐푡푎푛푔푙푒) = (6)(24) = 144 Units must be converted to inches first! 1 퐴푟푒푎(푇푟𝑖푎푛푔푙푒) = ( ) (13)(16) = 104 2 퐴푟푒푎 (푂푣푒푟푙푎푝) = (6)(4) = 24

퐴푟푒푎 (퐴푟푟표푤) = 144 + 104 − 24 = 224 𝑖푛2

HOMEWORK Problem Set Module 3 Lesson 2, page 12 #1, #2, #3, and #4. Round answers to the nearest whole unit. Show all in an organized and linear manner. DUE: Wednesday, February 13, 2017

MOD3 L2 3