anonymous
  • anonymous
How would I do this problem? In trapezoid PQRS, PQ is parallel to SR. Find the area of PQRS. Leave your answer is simplest radical form.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
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anonymous
  • anonymous
ok so do you know 30 60 90 triangles?
anonymous
  • anonymous
Yes

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anonymous
  • anonymous
more importantly do you know the sides ratio
anonymous
  • anonymous
Explain please.
anonymous
  • anonymous
well if i have a 30 60 90triangle and the side opposite to the 30 degrees is 1 what is the measure of the side opposite to the angle 60 degrees
anonymous
  • anonymous
2
anonymous
  • anonymous
good, so in your drawing, if i draw a line from the top edge (PQ) straight to the bottom edge (SR) i create a 30 60 90 right?
anonymous
  • anonymous
Right
anonymous
  • anonymous
so what is the measure of this newly created side call it h
anonymous
  • anonymous
I don't know
anonymous
  • anonymous
note that this side is opposite to the 30 degree angle
anonymous
  • anonymous
So it would be 8?
anonymous
  • anonymous
well give me a sec to draw this
anonymous
  • anonymous
|dw:1370562382480:dw|
anonymous
  • anonymous
so h is 12sqrt3?
anonymous
  • anonymous
oops i messed up the drawing! i am very sorry
anonymous
  • anonymous
let me try again
anonymous
  • anonymous
|dw:1370562630602:dw|
anonymous
  • anonymous
So it is just 12?
anonymous
  • anonymous
yes, Now do you know the formula for the area of the trapezoid?
anonymous
  • anonymous
Yes
anonymous
  • anonymous
so, that h we found is the height in the formula, do we need any other quantities for the formula?
anonymous
  • anonymous
Yea. the bottom base.
anonymous
  • anonymous
any ideas on how to get it?
anonymous
  • anonymous
No, but i know that 12sqrt3 is part of it
anonymous
  • anonymous
good that is right!
anonymous
  • anonymous
what if we try something like |dw:1370563102912:dw|
anonymous
  • anonymous
now we have a 45 45 90 triangle
anonymous
  • anonymous
right?
anonymous
  • anonymous
ya.
anonymous
  • anonymous
so what is the length of the opposite side to the bottom 45 degree angle?
anonymous
  • anonymous
12?
anonymous
  • anonymous
yes so that makes the bottom base equal to?
anonymous
  • anonymous
18?
anonymous
  • anonymous
nope, the bottom one
anonymous
  • anonymous
|dw:1370563522675:dw|
anonymous
  • anonymous
6?
anonymous
  • anonymous
actually is 6+12sqrt(3)
anonymous
  • anonymous
do you see why?
anonymous
  • anonymous
yeah
anonymous
  • anonymous
So it is 144 +72sqrt3
anonymous
  • anonymous
yep you got it :)

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