Trapezoid

parulmahajan89 wrote:In a Triangle abc,BE is // to CD, CD=20,BC=AB=6,AE=8 What is the area of trapezoid BEDC?

1)24
2)48
3)66
4)72
5)144

Not sure which approach to apply here? Should I take area of bigger triangle minus area of smaller triangle?

Dear parulmahajan89,
I'm happy to respond.

I don't think the problem is well specified. First of all, the direction of line segments is not clear --- for example, should D be on the same side of the triangle as E, or the opposite side??

Furthermore, I made two diagrams that conform to the specifications given in the problem, and there's still enough leeway for them to have very different areas.

I think this problem needs a diagram, and I think more information needs to be specified, before it is a well-defined problem that has a meaningful answer.

Mike

parulmahajan89 wrote:In a Triangle abc,BE is // to CD, CD=20,BC=AB=6,AE=8 What is the area of trapezoid BEDC?

1)24
2)48
3)66
4)72
5)144

Not sure which approach to apply here? Should I take area of bigger triangle minus area of smaller triangle?

Ah! Many thanks to Bill for the clarification. A picture is worth a thousand words. Just a note to parulmahajan89: any diagram that accompanies a GMAT math question inevitably contains information that is not reproduced in the verbal prompt; therefore, presenting the verbal prompt without the picture will inevitably be incomplete.

With the diagram, I see this is actually a brilliantly designed question. The first part of the solution involves the properties of similarity. See:
https://magoosh.com/gmat/2013/gmat-math-similar-shapes/
We know that ABE and ACD are similar triangles, and because AB = 6 and AC = 12, we know they are in a 1-to-2 ratio. That means, since AE = 8, AD = 16, and since CD = 20, BE = 10.

The next step is to realize that triangle ABE is a 6-8-10 right triangle, with a right angle at A, and triangle ACD is a 12-16-20 right triangle (these are 3-4-5 triangles multiplied, respectively, by 2 and 4). See:
https://magoosh.com/gmat/2012/pythagorea ... -the-gmat/

Thus, the area of ABC = 0.5bh = 0.5(6)(8) = 24, and the area of ACD = 0.5(12)(16) = 96, so as you suggest, the area of the trapezoid is simply the difference, 96 - 24 = 72. Answer = (D).

Does all this make sense?
Mike