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  • one year ago

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  1. anonymous
    • one year ago
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    ABCD is a parallelogram Which is greater a. The area of ABCD b. 24 |dw:1437774703693:dw|

  2. freckles
    • one year ago
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    do you know how to find the area of parallelogram ? |dw:1437775012406:dw|

  3. freckles
    • one year ago
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    where the area is b*h

  4. freckles
    • one year ago
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    we are actually given b is 4

  5. freckles
    • one year ago
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    can you find h?

  6. anonymous
    • one year ago
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    how do i find h?

  7. freckles
    • one year ago
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    you could use a trig ratio you know an angle and you also know the hyp of the triangle I drew inside the parallelogram

  8. freckles
    • one year ago
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    the opp of that angle is the thing you want to find

  9. freckles
    • one year ago
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    opp and hyp think sin( )

  10. anonymous
    • one year ago
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    wait.... I cant use sin we don't use that it has to be an alternative method...

  11. freckles
    • one year ago
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    ok what is the alternative method?

  12. anonymous
    • one year ago
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    im not sure it has to be done without sin tho...

  13. freckles
    • one year ago
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    oh then I don't know of another way to find the area

  14. anonymous
    • one year ago
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    crap... it's talking about the area of the parallelogram is equal to the length of base AD which is 4 times the height which is less than 6

  15. freckles
    • one year ago
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    ok

  16. anonymous
    • one year ago
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    Since the product of 4 and a number less than 6 must be less than 24, the area of the parallelogram must be less than 24.

  17. freckles
    • one year ago
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    so we don't need to find the area exactly

  18. freckles
    • one year ago
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    we can approximate it

  19. anonymous
    • one year ago
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    what does this all mean..

  20. freckles
    • one year ago
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    |dw:1437775540138:dw| anyways .... by Pythagorean theorem we have \[h=\sqrt{36-a^2} \\ \text{ so area of parallelogram is } 4 \cdot h=4 \cdot \sqrt{36-a^2} \\ \text{ and we know that } 0<a<6 \\ \text{ so } \\ 4 \cdot h=4 \sqrt{36-a^2} <4 \sqrt{36-0^2}=4 \sqrt{36}=... \] cam you finish simplifying this

  21. anonymous
    • one year ago
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    24

  22. freckles
    • one year ago
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    right 4*h<24

  23. freckles
    • one year ago
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    where 4*h is the area of the parallelogram

  24. freckles
    • one year ago
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    didn't label what I called a by the way |dw:1437775996191:dw| I used Pythagorean theorem

  25. freckles
    • one year ago
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    \[6^2=h^2+a^2 \\ 6^2-a^2=h^2 \\ \sqrt{6^2-a^2}=h\]

  26. anonymous
    • one year ago
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    hmmmmm i think i get it now..

  27. freckles
    • one year ago
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    and I wanted the thing inside the square root to be positive and I also want a to be positive because a represents a measurement

  28. freckles
    • one year ago
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    \[6^2-a^2>0 \text{ and } a>0 \\ 6^2>a^2 \text{ and } a>0 \\ 36>a^2 \text{ and } a>0 \\ \text{ solving } a^2<36 \text{ means we have } -6< a<6 \\ \text{ but remember we also need} a>0 \\ \text{ so we need } 0<a<6\]

  29. anonymous
    • one year ago
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    ok

  30. freckles
    • one year ago
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    and if we multiply both sides by -1 we have \[-6<-a<0 \\ \text{ so back to the inequality } \\ 4 h=4 \sqrt{36-a^2}<4 \sqrt{36-0^2}\]

  31. freckles
    • one year ago
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    but yeah I would have used my trigonometry knowledge :p

  32. anonymous
    • one year ago
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    this is complicated I'm gonna sit and stare at this for a while.

  33. freckles
    • one year ago
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    \[4h=4 \cdot 6 \sin(55)=24\sin(55) \approx 19.66 \]

  34. freckles
    • one year ago
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    all you have to know is that since h is between 0 and 6 (not including 6) we have 4h<4(6)

  35. anonymous
    • one year ago
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    hmmm... ok got it

  36. freckles
    • one year ago
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    how about we say something in general... |dw:1437776683255:dw| so the simplest way I can write this for your problem is: |dw:1437776770728:dw|

  37. freckles
    • one year ago
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    and we know a>h because in the right triangle we drew we have a is the hyp or in your example 6 is the hyp

  38. freckles
    • one year ago
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    anyways I think I'm done now :) unless you have questions

  39. anonymous
    • one year ago
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    ohhhh okay i think i understand better now

  40. anonymous
    • one year ago
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    needed that visual thank you ^_^

  41. freckles
    • one year ago
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    visuals are the secret to math

  42. anonymous
    • one year ago
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    agreed!!

  43. freckles
    • one year ago
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    I think it helps to know the hyp is the longest side in a right triangle on this question

  44. anonymous
    • one year ago
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    yea definitely helps

  45. freckles
    • one year ago
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    but in all fairness to you I think I started with a complicated reason but the last reason I gave I think is definitely less complicated

  46. anonymous
    • one year ago
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    yea it helped towards the end thanks again =)

  47. freckles
    • one year ago
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    np

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