1. 3.2 How Can I Find the Height? Pg. 6 Heights and Areas of Triangles

2. 3.2 – How Can I Find the Height?__________ Heights and Area of Triangles Sometimes the height of a shape isn't shown in the picture. Today we are going to examine how to find the height of a shape when it isn't shown.

3. 3.8 –HEIGHT LAB What is the height of a triangle? Is it like walking up any side of the triangle? Or is it like standing at the highest point and looking straight down? Today your team will build triangles with string and consider different ways heights can be seen for triangles of various shapes.

4. a. Use the materials given to you by your teacher to make a triangle like the one in the diagram below. Be sure to use the team roles listed below.

5. Resource Manager: Holds the two bottom corners, forming the base of the triangle Facilitator: Makes sure the red string dangles down freely, not touching anything Recorder/Reporter: Sketches the triangles that are created, shares them with the team when group is finished Team Captain: Makes the third point (top point) of the triangle and the height string with pencil or pen

7. b. Now, with your team, build and sketch triangles that meet the three conditions below.

9. 3.9 –HEIGHT HUNT How can I find the height of a triangle if it is not a right triangle? a. Assume you know the length of the side labeled "base." For each triangle, draw in the height that would enable you to find the area of the triangle. A notecard can be used to translate along the base until you reach the height. Note: You do not need to find the area.

15. b. For the triangle below, draw all three possible heights. First choose one side to be the base and draw in the corresponding height. Then repeat the process of drawing in the height for the other two sides, one at a time.

16. base

20. 3.10 –AREA OF SHADED PART Find the area of the shaded figure. Be ready to share any observations.

21. 3.11 –AREA OF A TRIANGLE Isaiah claimed that he didn't need to calculate the area for (b) and (c) because it must be the same as the area for the triangle in part (a). a. Is Isaiah's claim correct? How do you know? Yes, they are all half of the same rectangle

22. b. Explain why the area of any triangle is half the area of a rectangle that has the same base and height. That is, show that the area of a triangle must be http://hotmath.com/util/hm_flash_movie_full. html?movie=/hotmath_help/gizmos/triangleA rea.swf Area of Triangle

27. They all have the same area

28. 3.12 –AREA OF A TRIANGLE, CONT How do you know which dimensions to use when finding the area of a triangle? a. Find the area of each shaded figure. Draw any lines on the paper that will help. Turning the triangles may help you discover a way to find their areas.

29. A = ½bh A = ½(21)(12) A = ½(252) A = 126un 2

30. A = ½bh A = ½(6)(5) A = (3)(5) A = 15un 2

31. A = ½bh A = ½(7)(8) A = ½(56) A = 28un 2 7 8

32. b. Look back at your work from part (a). Which numbers from each triangle did you use to find the area? Write an explanation and/or draw a diagram that would help another student understand how to choose which lengths to use when calculating the area. b h

33. c. Mario, Raquel, and Jocelyn are arguing about where the height is for the triangle below. The three have written their names along the part they think should be the height. Determine which person is correct. Explain why the one you chose is correct and why the other two are incorrect.