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anonymous

  • one year ago

In trapezoid PQRS, PQ is parallel to SR. What is the area of PQRS in simplest radical form?

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  1. anonymous
    • one year ago
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  2. anonymous
    • one year ago
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    i got the height as 16 ?? idk how to get the bottom base can someone help

  3. jim_thompson5910
    • one year ago
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    |dw:1433379207636:dw|

  4. jim_thompson5910
    • one year ago
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    |dw:1433379358414:dw| you have the correct height, TQ = 16

  5. jim_thompson5910
    • one year ago
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    what is the distance from T to R?

  6. anonymous
    • one year ago
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    i got 27.71281292 ??

  7. jim_thompson5910
    • one year ago
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    triangle TRQ is a 30-60-90 triangle, so you'll find that TQ = 16 \(\large TR = 16\sqrt{3}\) |dw:1433380082720:dw|

  8. jim_thompson5910
    • one year ago
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    now construct a perpendicular segment to PQ that goes through point S |dw:1433380133685:dw| mark the new point point U as shown above

  9. jim_thompson5910
    • one year ago
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    angle UST = 90 degrees since I made SU perpendicular to PQ |dw:1433380192075:dw| so that means angle PSU must be 45 degrees (45+90 = 135)

  10. jim_thompson5910
    • one year ago
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    |dw:1433380223132:dw|

  11. jim_thompson5910
    • one year ago
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    agreed so far?

  12. anonymous
    • one year ago
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    ya

  13. jim_thompson5910
    • one year ago
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    TQ = SU since SUQT is a rectangle so SU = 16 SU = PU due to the fact that PSU is a 45-45-90 triangle PU = 16 as well

  14. jim_thompson5910
    • one year ago
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    |dw:1433380378598:dw|

  15. jim_thompson5910
    • one year ago
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    |dw:1433380396688:dw|

  16. jim_thompson5910
    • one year ago
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    UQ = 8 and ST = 8 because UQ = ST |dw:1433380435649:dw|

  17. jim_thompson5910
    • one year ago
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    So all of that allows us to conclude that \[\Large SR = 8+16\sqrt{3} \approx 35.71281\]

  18. anonymous
    • one year ago
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    for the area i got \[A \approx 477.7\]

  19. anonymous
    • one year ago
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    in the simplest radical form it would be 256+128sqrt3 ?

  20. jim_thompson5910
    • one year ago
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    yep \[\Large 256+128\sqrt{3}\] is the answer they want

  21. jim_thompson5910
    • one year ago
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    and \[\Large 256+128\sqrt{3} \approx 477.7025034\] is the approximate area

  22. anonymous
    • one year ago
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    okay!! thank you so much :D

  23. jim_thompson5910
    • one year ago
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    yw

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