Area of Right Triangles

Warm Up A = b x h A = 25 x 8 height A = 200 ft2 base OBJECTIVE: SWBAT determine the area of any right triangle and defend their method. 1) What is the Area of the Parallelogram below? A = b x h A = 25 x 8 A = 200 ft2 10 ft 8 ft height base 25 ft Calculate         (Click for Detailed Solutions)

Getting Ready– Puzzle! 1) How many rectangles can you find? What are their areas? Hints

Getting Ready – Puzzle! 2) How many shapes can you find? Name them if you can. Hints

Launch This is a right triangle. What is a right triangle? A right triangle is a triangle that has one 90⁰ angle. What is the area of this right triangle? How do you know? How can you show your work/prove your answer? = 1 square unit

Launch What is the area of the shaded region? How do you know? How can you show your work/prove your answer?

Explore – Understanding the Strategy Angela’s Strategy Draw a “surrounding rectangle” Determine the area of the rectangle The area of the triangle is half the area of the rectangle! Do you understand Angela’s strategy?

Explore - More Part 3 - (10 Min) Finish the worksheet in GROUPS Use Angela’s Strategy to find the area of the remaining triangles on the worksheet. 1-Partners 2-Strategy Check 3-Groups

Summary – Complete 1 – 14 with your group – showing all of your work. 9) 10) 11) 1) 2) 4) 3) 12) 13) 14) 5) 6) 7) 8) To Explore

Summary (Part 2) Explain the Strategy Turn and Talk: Common Language: Lefty, tell Righty the strategy for finding the area of ANY right triangle. Righty, tell Lefty the strategy. Common Language: Can you explain the strategy we learned that will work for finding the area of ANY right triangle? Why does this strategy work?

Summary (Part 2) Expand your Thinking Does this strategy work when there are no grid lines?

Area of “Rectangle”: 5 ft x 10 ft = 50 ft2 Area of Triangle Summary (Part 2) Draw and label a triangle with a base of 5 ft and a height of 10 ft. Then find the area. Area of “Rectangle”: 5 ft x 10 ft = 50 ft2 Area of Triangle 50 ft2 ÷ 2 = 25 ft2 10 ft Oh yeah… Half of 50 is 25! 5 ft Hmmm…

Summary (Part 2) Practice – in your journal #1) Draw and label a triangle with a base of 8 in and a height of 3 in. Then find the area. Area of “Rectangle”: 8 in x 3 in = 24 in2 Area of Triangle 24 in2 ÷ 2 = 12 in2 3 in 8 in Oh yeah… Half of 24 is 12! Hmmm…

Summary (Part 2) Practice – in your journal #2) 8 ft 5 ft Rectangle area = ______ Triangle area = ______ #3) 12 m 4 m Triangle area = _______ Rectangle area = ______ 40 ft2 48 m2 20 ft2 24 m2

Complete 15 – 17 with your group. Should everyone’s triangle look the same? Do they need to??

Exit Ticket - in your journal 4 cm What is the area of the “Surrounding Rectangle” for this Right Triangle? 9 cm 13 cm2 18 cm2 36 cm2 d) 25 cm2

Exit Ticket - in your journal 4 cm What is the area of the Triangle? 9 cm 4 ½ cm2 18 cm2 36 cm2 d) 11 cm2