Chapter 11 Areas of Plane Figures

1. Chapter 11Areas of Plane Figures • Understand what is meant by the area of a polygon. • Know and use the formulas for the areas of plane figures. • Work geometric probability problems.

2. 11-1: Area of Rectangles Objectives • Learn and apply the area formula for a square and a rectangle.

3. A measurement of the region covered by a geometric figure and its interior. Area

4. The area of a rectangle is the product of the base and height. Theorem h Area = b x h b

5. Base • Any side of a rectangle or other parallelogram can be considered to be a base.

6. Altitude • Altitude to a base is any segment perpendicular to the line containing the base from any point on the opposite side. • Called Height

7. Postulate The area of a square is the length of the side squared. Area = s2 s s

8. Postulate If two figures are congruent, then they have the same area. B A If triangle A is congruent to triangle B, then area A = area B.

9. Find the area ???

10. The area of a region is the sum of the areas of its non-overlapping parts Area Addition Postulate B A C

11. Remote Time Classify each statement as True or False

12. Question 1 • If two figures have the same areas, then they must be congruent.

13. Question 2 • If two figures have the same perimeter, then they must have the same area.

14. Question 3 • If two figures are congruent, then they must have the same area.

15. Question 4 • Every square is a rectangle.

16. Question 5 • Every rectangle is a square.

17. Question 6 • The base of a rectangle can be any side of the rectangle.

18. White Board Practice h b

19. White Board Practice h b

20. Group Practice • Find the area of the figure. Consecutive sides are perpendicular. 3 2 5 4 5 6

21. Group Practice • Find the area of the figure. Consecutive sides are perpendicular. 3 2 5 4 5 A = 114 6

22. 11-2: Areas of Parallelograms, Triangles, and Rhombuses Objectives • Determine and apply the area formula for a parallelogram, triangle and rhombus.

23. Tons of formulas to memorize • So don’t memorize them • Understand them !

24. Refresh my memory… What is the area of a rectangle ? A = bh

25. Refresh my memory… what is the height in a rectangle? Altitude to a base is any segment perpendicular to the line containing the base from any point on the opposite side.

27. h

29. h

30. h

31. Cut h Slide over and tape

32. h

33. Do we have any leftover paper? NO !

34. So this means the area must be the same Area of Rectangle = Area of Parallelogram

35. Theorem The area of a parallelogram is the product of the base times the height to that base. h Area = b x h b

36. But Wait…. Cut Here

37. What do we have ? X 2

38. Theorem The area of a triangle equals half the product of the base times the height to that base. h b

39. Theorem The area of a rhombus equals half the product of the diagonals. d1 d2

40. Remote Time

41. White Board Practice • Find the area of the figure 4 4 4

42. White Board Practice • Find the area of the figure 4 4 4

43. White Board Practice • Find the area of the figure 6 3 3 60º 6

44. White Board Practice • Find the area of the figure 6 3 3 60º 6

45. White Board Practice • Find the area of the figure 5 5 6

46. White Board Practice • Find the area of the figure 5 5 6

47. White Board Practice • Find the area of the figure 2 5 2 5

48. White Board Practice • Find the area of the figure 2 5 2 5

49. White Board Practice • Find the area of the figure 5 4 5 5 4 5

50. White Board Practice • Find the area of the figure 5 4 5 5 4 5