anonymous
  • anonymous
In trapezoid PQRS, PQ is parallel to SR. What is the area of PQRS in simplest radical form?
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
anonymous
  • anonymous
i got the height as 16 ?? idk how to get the bottom base can someone help
jim_thompson5910
  • jim_thompson5910
|dw:1433379207636:dw|

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jim_thompson5910
  • jim_thompson5910
|dw:1433379358414:dw| you have the correct height, TQ = 16
jim_thompson5910
  • jim_thompson5910
what is the distance from T to R?
anonymous
  • anonymous
i got 27.71281292 ??
jim_thompson5910
  • jim_thompson5910
triangle TRQ is a 30-60-90 triangle, so you'll find that TQ = 16 \(\large TR = 16\sqrt{3}\) |dw:1433380082720:dw|
jim_thompson5910
  • jim_thompson5910
now construct a perpendicular segment to PQ that goes through point S |dw:1433380133685:dw| mark the new point point U as shown above
jim_thompson5910
  • jim_thompson5910
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)
jim_thompson5910
  • jim_thompson5910
|dw:1433380223132:dw|
jim_thompson5910
  • jim_thompson5910
agreed so far?
anonymous
  • anonymous
ya
jim_thompson5910
  • jim_thompson5910
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
jim_thompson5910
  • jim_thompson5910
|dw:1433380378598:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1433380396688:dw|
jim_thompson5910
  • jim_thompson5910
UQ = 8 and ST = 8 because UQ = ST |dw:1433380435649:dw|
jim_thompson5910
  • jim_thompson5910
So all of that allows us to conclude that \[\Large SR = 8+16\sqrt{3} \approx 35.71281\]
anonymous
  • anonymous
for the area i got \[A \approx 477.7\]
anonymous
  • anonymous
in the simplest radical form it would be 256+128sqrt3 ?
jim_thompson5910
  • jim_thompson5910
yep \[\Large 256+128\sqrt{3}\] is the answer they want
jim_thompson5910
  • jim_thompson5910
and \[\Large 256+128\sqrt{3} \approx 477.7025034\] is the approximate area
anonymous
  • anonymous
okay!! thank you so much :D
jim_thompson5910
  • jim_thompson5910
yw

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