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J.L.

  • 3 years ago

PLEASE HELP! The figure below shows AB = 4 units and BD = 6 units. If the area of triangle ADE is 50 square units, what is the area of the trapezoid BCED? 40 square units 44 square units 48 square units 42 square units http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/pool_Geom_3641_Seg_Two_Exam_35/image0034e9d7dd7.jpg

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  1. Calcmathlete
    • 3 years ago
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    Are you familiar with the concept that similar figures have a ratio for area?

  2. lgbasallote
    • 3 years ago
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    de javu

  3. J.L.
    • 3 years ago
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    Yea

  4. Calcmathlete
    • 3 years ago
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    I mean as in if there is a ratio between side lengths a : b, then the ratio fo the areas is \(a^2 : b^2\)

  5. lgbasallote
    • 3 years ago
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    im thinking area of big triangle - area of small triangle = area of trapezoid

  6. J.L.
    • 3 years ago
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    Yea I know what you're talking about @Calcmathlete

  7. Calcmathlete
    • 3 years ago
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    Yup. First you have to find the area of the smaller triangle though. If a : b is 2 : 5, then what is \(a^2 : b^2\)?

  8. J.L.
    • 3 years ago
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    4:25

  9. lgbasallote
    • 3 years ago
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    how did you get 2:5 again?

  10. J.L.
    • 3 years ago
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    Shouldn't it be 4:5?

  11. Calcmathlete
    • 3 years ago
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    The ratio of the similar triangles lgba. Now, set up a proportion between the two areas. \[\frac{4}{25} = \frac{x}{50}\]Solve for x.

  12. Calcmathlete
    • 3 years ago
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    Why do you say it should be 4 : 5?

  13. J.L.
    • 3 years ago
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    Because that's the ratio of the corresponding sides...CB=4 and BE=5 so the ratio would be 4:5 or 0.8

  14. Calcmathlete
    • 3 years ago
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    Are we looking at the same picture?

  15. J.L.
    • 3 years ago
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    Sorry I was looking at a different question haha

  16. J.L.
    • 3 years ago
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    shouldn't it be 4:6 then or 2:3?

  17. Calcmathlete
    • 3 years ago
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    Not quite. That isn't the ratio of the triangles. Think about it. 6 is a part of the side of a triangle. Not the actual triangle.

  18. J.L.
    • 3 years ago
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    Okay got it x=8

  19. Calcmathlete
    • 3 years ago
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    Ok. Now subtract the areas of the two triangles.

  20. J.L.
    • 3 years ago
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    I know the area of the first triangle is 50...what's the area of the second?

  21. Calcmathlete
    • 3 years ago
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    Area of the second triangle = 8

  22. J.L.
    • 3 years ago
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    Ohhh 50-8=42

  23. Calcmathlete
    • 3 years ago
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    There you go :)

  24. J.L.
    • 3 years ago
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    You are truly awesome

  25. Calcmathlete
    • 3 years ago
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    lol Thanks @lgbasallote Clearly you need to brush up on those geometry skills ;)

  26. lgbasallote
    • 3 years ago
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    ...clearly...

  27. lgbasallote
    • 3 years ago
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    hmm it always is 42 huh

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