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by Arcane66 » Thu Sep 09, 2010 8:48 am
is the answer A?
I think that from the figure you can put 4 in as the height, drawn down from A & B as 4. You are also given that B is 120 degrees. I think that the first statement is enough because you can already tell that the two triangles of this shape are in the form 30-60-90. ie. angles are x,xsqrt3,2x. I don't know though, I could be wrong.
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by InkyBinky » Thu Sep 09, 2010 9:49 am
I say C. A trapezoid only requires the two bases to be parallel, but the sides don't have to be of equal length. If we knew the sides were of equal length, then (A) would be sufficient. But since we do not know that, we can't figure out the length of the bottom base. (B) is insufficient because it doesn't give a length. However, because ADC is 60 and the bases are parallel, we know that the upper-left angle is 120 degrees. Since the upper right is 120 degrees, we know that the two sides are of equal length. Using that information and the length of the upper base, we can use a 30-60-90 triangle to derive the length of the bottom. We then have the lengths of both bases and the height, which is sufficient to determine the area of a trapezoid.
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by lokesh r » Thu Sep 09, 2010 2:13 pm
Area of a trapezoid = average of bases x height.

Question states that height=4.

From A. Base1=5

angle ABC=120.

Draw straight line from vertices B touching DC perpendicularly, say at E.

So Angle CBE=30.

(Please draw diagram)

Now BE =4, Apply 30-60-90 rule. BE=4/sqrt(3).

Base2= 5+ 2x4/sqrt(3).

So at this point we have base 1, base 2 and height which are enought to calculate area of trapezoid.

From B. Nothing can be deduced.

So answer would be A.
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by InkyBinky » Thu Sep 09, 2010 5:05 pm
lokesh r wrote: Base2= 5+ 2x4/sqrt(3).
This is an erroneous assumption. The problem doesn't say that the trapezoid is symmetrical, so you can't assume that both the left and right hand sides are of equal length. You need to know an angle or some other information to determine the length of the left-hand side.
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by uwhusky » Thu Sep 09, 2010 5:11 pm
Agreed with everything Inky said, C.
Yep.
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by lokesh r » Fri Sep 10, 2010 12:10 pm
Thanks inkybinky for reminding a very good rule.

So area of trapezoid=average of bases x height applies only for symmetrical trapezoid.

So i agree with you that answer is C.

Official Answer pls..........
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