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# Area Formulas

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### Area Formulas

1. 1. Area Formulas Made by Jennifer Jasensky
2. 2. Rectangle
3. 3. Rectangle What is the area formula?
4. 4. Rectangle What is the area formula? bh
5. 5. Rectangle What is the area formula? bh What other shape has 4 right angles?
6. 6. Rectangle What is the area formula? bh What other shape has 4 right angles? Square!
7. 7. Rectangle What is the area formula? bh What other shape has 4 right angles? Square! Can we use the same area formula?
8. 8. Rectangle What is the area formula? bh What other shape has 4 right angles? Square! Can we use the same area formula? Yes
9. 9. Practice! Rectangle Square 10m 17m 14cm
10. 10. Answers Rectangle Square 10m 17m 14cm 196 cm 2 170 m 2
11. 11. So then what happens if we cut a rectangle in half? What shape is made?
12. 12. Triangle So then what happens if we cut a rectangle in half? What shape is made?
13. 13. Triangle So then what happens if we cut a rectangle in half? What shape is made? 2 Triangles
14. 14. Triangle So then what happens if we cut a rectangle in half? What shape is made? 2 Triangles So then what happens to the formula?
15. 15. Triangle So then what happens if we cut a rectangle in half? What shape is made? 2 Triangles So then what happens to the formula?
16. 16. Triangle So then what happens if we cut a rectangle in half? What shape is made? 2 Triangles So then what happens to the formula? bh
17. 17. Triangle So then what happens if we cut a rectangle in half? What shape is made? 2 Triangles So then what happens to the formula? bh 2
18. 18. Practice! Triangle 5 ft 14 ft
19. 19. Answers 35 ft 2 Triangle 5 ft 14 ft
20. 20. Summary so far... <ul><li>bh </li></ul>
21. 21. Summary so far... <ul><li>bh </li></ul>
22. 22. Summary so far... <ul><li>bh </li></ul>
23. 23. Summary so far... <ul><li>bh </li></ul>bh
24. 24. Summary so far... <ul><li>bh </li></ul>bh 2
25. 25. Parallelogram Let’s look at a parallelogram.
26. 26. Parallelogram Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends?
27. 27. Parallelogram Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends?
28. 28. Parallelogram Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends?
29. 29. Parallelogram Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends?
30. 30. Parallelogram Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends?
31. 31. Parallelogram Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends?
32. 32. Parallelogram Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends?
33. 33. Parallelogram Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends?
34. 34. Parallelogram Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends?
35. 35. Parallelogram Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends?
36. 36. Parallelogram Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends? What will the area formula be now that it is a rectangle?
37. 37. Parallelogram Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends? What will the area formula be now that it is a rectangle? bh
38. 38. Parallelogram Be careful though! The height has to be perpendicular from the base, just like the side of a rectangle! bh
39. 39. Parallelogram Be careful though! The height has to be perpendicular from the base, just like the side of a rectangle! bh
40. 40. Parallelogram Be careful though! The height has to be perpendicular from the base, just like the side of a rectangle! bh
41. 41. Rhombus The rhombus is just a parallelogram with all equal sides! So it also has bh for an area formula. bh
42. 42. Practice! Parallelogram Rhombus 3 in 9 in 4 cm 2.7 cm
43. 43. Answers 10.8 cm 2 27 in 2 Parallelogram Rhombus 3 in 9 in 4 cm 2.7 cm
44. 44. Let’s try something new with the parallelogram.
45. 45. Let’s try something new with the parallelogram. Earlier, you saw that you could use two trapezoids to make a parallelogram.
46. 46. Let’s try something new with the parallelogram. Earlier, you saw that you could use two trapezoids to make a parallelogram. Let’s try to figure out the formula since we now know the area formula for a parallelogram.
47. 47. Trapezoid
48. 48. Trapezoid
49. 49. Trapezoid So we see that we are dividing the parallelogram in half. What will that do to the formula?
50. 50. Trapezoid So we see that we are dividing the parallelogram in half. What will that do to the formula? bh
51. 51. Trapezoid So we see that we are dividing the parallelogram in half. What will that do to the formula? bh 2
52. 52. Trapezoid But now there is a problem. What is wrong with the base? bh 2
53. 53. Trapezoid b h 2 So we need to account for the split base, by calling the top base, base 1 , and the bottom base, base 2 . By adding them together, we get the original base from the parallelogram. The heights are the same, so no problem there.
54. 54. Trapezoid ( b1 + b2 ) h 2 So we need to account for the split base, by calling the top base, base 1 , and the bottom base, base 2 . By adding them together, we get the original base from the parallelogram. The heights are the same, so no problem there. base 2 base 1 base 1 base 2
55. 55. Practice! Trapezoid 11 m 3 m 5 m
56. 56. Answers 35 m 2 Trapezoid 11 m 3 m 5 m
57. 57. Summary so far... <ul><li>bh </li></ul>
58. 58. Summary so far... <ul><li>bh </li></ul>
59. 59. Summary so far... <ul><li>bh </li></ul>
60. 60. Summary so far... <ul><li>bh </li></ul>bh
61. 61. Summary so far... <ul><li>bh </li></ul>bh 2
62. 62. Summary so far... <ul><li>bh </li></ul>bh 2
63. 63. Summary so far... <ul><li>bh </li></ul>bh 2
64. 64. Summary so far... <ul><li>bh </li></ul>bh 2
65. 65. Summary so far... <ul><li>bh </li></ul>bh 2
66. 66. Summary so far... <ul><li>bh </li></ul>bh 2
67. 67. Summary so far... <ul><li>bh </li></ul>bh 2
68. 68. Summary so far... <ul><li>bh </li></ul>bh 2
69. 69. Summary so far... <ul><li>bh </li></ul>bh 2
70. 70. Summary so far... <ul><li>bh </li></ul>bh 2
71. 71. Summary so far... <ul><li>bh </li></ul>bh 2 ( b1 + b2 ) h 2
72. 72. Summary so far... <ul><li>bh </li></ul>bh 2 ( b1 + b2 ) h 2
73. 73. Summary so far... <ul><li>bh </li></ul>bh 2 ( b1 + b2 ) h 2
74. 74. Summary so far... <ul><li>bh </li></ul>bh 2 ( b1 + b2 ) h 2
75. 75. Summary so far... <ul><li>bh </li></ul>bh 2 ( b1 + b2 ) h 2
76. 76. Summary so far... <ul><li>bh </li></ul>bh 2 ( b1 + b2 ) h 2
77. 77. So there is just one more left!
78. 78. So there is just one more left! Let’s go back to the triangle. A few weeks ago you learned that by reflecting a triangle, you can make a kite.
79. 79. Kite So there is just one more left! Let’s go back to the triangle. A few weeks ago you learned that by reflecting a triangle, you can make a kite.
80. 80. Kite Now we have to determine the formula. What is the area of a triangle formula again?
81. 81. Kite Now we have to determine the formula. What is the area of a triangle formula again? b h 2
82. 82. Kite Now we have to determine the formula. What is the area of a triangle formula again? b h 2 Fill in the blank. A kite is made up of ____ triangles.
83. 83. Kite Now we have to determine the formula. What is the area of a triangle formula again? b h 2 Fill in the blank. A kite is made up of ____ triangles. So it seems we should multiply the formula by 2.
84. 84. Kite b h 2 *2 = b h
85. 85. Kite Now we have a different problem. What is the base and height of a kite? The green line is called the symmetry line, and the red line is half the other diagonal. b h 2 *2 = b h
86. 86. Kite Let’s use kite vocabulary instead to create our formula. Symmetry Line* Half the Other Diagonal
87. 87. Practice! Kite 2 ft 10 ft
88. 88. Answers 20 ft 2 Kite 2 ft 10 ft
89. 89. Summary so far... <ul><li>bh </li></ul>
90. 90. Summary so far... <ul><li>bh </li></ul>
91. 91. Summary so far... <ul><li>bh </li></ul>
92. 92. Summary so far... <ul><li>bh </li></ul>bh
93. 93. Summary so far... <ul><li>bh </li></ul>bh 2
94. 94. Summary so far... <ul><li>bh </li></ul>bh 2
95. 95. Summary so far... <ul><li>bh </li></ul>bh 2
96. 96. Summary so far... <ul><li>bh </li></ul>bh 2
97. 97. Summary so far... <ul><li>bh </li></ul>bh 2
98. 98. Summary so far... <ul><li>bh </li></ul>bh 2
99. 99. Summary so far... <ul><li>bh </li></ul>bh 2
100. 100. Summary so far... <ul><li>bh </li></ul>bh 2
101. 101. Summary so far... <ul><li>bh </li></ul>bh 2
102. 102. Summary so far... <ul><li>bh </li></ul>bh 2
103. 103. Summary so far... <ul><li>bh </li></ul>bh 2 ( b1 + b2 ) h 2
104. 104. Summary so far... <ul><li>bh </li></ul>bh 2 ( b1 + b2 ) h 2
105. 105. Summary so far... <ul><li>bh </li></ul>bh 2 ( b1 + b2 ) h 2
106. 106. Summary so far... <ul><li>bh </li></ul>bh 2 ( b1 + b2 ) h 2
107. 107. Summary so far... <ul><li>bh </li></ul>bh 2 ( b1 + b2 ) h 2
108. 108. Summary so far... <ul><li>bh </li></ul>bh 2 ( b1 + b2 ) h 2
109. 109. Summary so far... <ul><li>bh </li></ul>bh 2 ( b1 + b2 ) h 2
110. 110. Summary so far... <ul><li>bh </li></ul>bh 2 ( b1 + b2 ) h 2
111. 111. Summary so far... <ul><li>bh </li></ul>bh 2 ( b1 + b2 ) h 2
112. 112. Summary so far... <ul><li>bh </li></ul>bh 2 ( b1 + b2 ) h 2 Symmetry Line * Half the Other Diagonal
113. 113. Final Summary Make sure all your formulas are written down! <ul><li>b h </li></ul>b h 2 ( b1 + b2 ) h 2 Symmetry Line * Half the Other Diagonal Made by Jennifer Jasensky