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Measurement

Measurement

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Measurement

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  1. Measurement

  2. Area of Square • Square A = l x w A = 4 x 4 W = 4 A = 16 units2 L = 4

  3. Area of Rectangle • Rectangle A = l x w A = 6 x 4 W = 4 A = 24 units2 L = 6

  4. Area of a Triangle • Triangle A = ½ (b x h) A = ½ (4 x 4) h = 4 A = ½ (16) A = 8 units2 b = 4

  5. Finding the Area of Regular Shapes • Square A = l x w • Rectangle A = l x w • Triangle A = ½ (b x h)

  6. Finding the Area of Composite Shapes

  7. Break the shape apart into shapes you know how to find the area of….

  8. Becomes………. +

  9. Becomes………. + +

  10. Becomes………. + +

  11. We can use this strategy to help us find the area of a parallelogram by changing the location of the end triangles + + + =

  12. Therefore the area of a parallelogram is….. A = b x h h = 3 b = 5

  13. Can we apply the same strategies to finding the area of a trapezoid……? b1 Where b1 and b2 represent the parallel sides h is the height h b2

  14. Using graph paper, draw a trapezoid with the following units… Now, see if you can break it apart into different shapes, rearrange and find a new formula…… b1 = 3 h= 4 b2 = 5

  15. Copy, Reflect, and Translate the trapezoid……what shape do you have now???? Do you know the formula for this new shape? How can you modify it for a TRAPEZOID? b1 = 3 h= 4 b2 = 5

  16. Now we have a parallelogram…. only it’s 2x’s as big as the trapezoid b1 = 3 h= 4 h= 4 b2 = 5 b2 = 5

  17. b2 = 5 b1 = 3 h= 4 b2 = 5 b1 = 3 The are of this PARALLELOGRAM is A = base x height A = (b1 + b2) x height

  18. b2 = 5 b1 = 3 h= 4 b2 = 5 b1 = 3 It doesn’t matter which type of trapezoid you use, copy, rotate and put the 2 together and you get a parrallelogram!!!! A = ½ [ (b1 + b2) x h ]

  19. b2 = 7 b1 = 3 h= 4 b2 = 7 b1 = 3 But, because the TRAPEZOID is only half the size of the parallelogram, we need to take half of the area….. A = (b1 + b2) x h 2

  20. b2 = 6 b1 = 3 h= 4 b2 = 6 b1 = 3 But, because the TRAPEZOID is only half the size of the parallelogram, we need to take half of the area….. A = (b1 + b2) x h 2

  21. A = ½ [ (b1 + b2) x h ] Or A = [ (b1 + b2) x h ] / 2 Or A = (b1 + b2) x h 2

  22. Is there another way???? b1 = 4 cm 3 cm b2 = 7 cm

  23. We can divide the trapezoid into 2 Triangles b1 = 4 cm 3 cm 3 cm b2 = 7 cm

  24. b1 = 4 cm 3 cm b2 = 7 cm 3 cm You should notice that the height should be the same for both triangles.

  25. b1 = 4 cm 3 cm b2 = 7 cm 3 cm Area = Triangle 1 + Triangle 2 A = b1 x h + b2 x h2 2

  26. b1 = 6 h= 8 b2 = 10 Find the area of the following Trapezoids. b1 = 2 h= 6 b2 = 8