BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Trapezoid

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 74
Joined: Fri May 11, 2012 9:06 pm

Trapezoid

by parulmahajan89 » Wed Feb 12, 2014 9:58 pm
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?
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 768
Joined: Wed Dec 28, 2011 4:18 pm
Location: Berkeley, CA
Thanked: 387 times
Followed by:140 members

by Mike@Magoosh » Thu Feb 13, 2014 4:39 pm
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 :-)
Attachments
Trapezoid CBED.JPG
Magoosh GMAT Instructor
https://gmat.magoosh.com/
Top
User avatar
GMAT Instructor
Posts: 1248
Joined: Thu Mar 29, 2012 2:57 pm
Location: Everywhere
Thanked: 503 times
Followed by:192 members
GMAT Score:780

by Bill@VeritasPrep » Fri Feb 14, 2014 11:20 am
I don't think the original version of this problem specifies triangle ABC, but it does provide you with this diagram.
Attachments
Screen Shot 2014-02-14 at 11.20.06 AM.png
trapezoid in triangle
Join Veritas Prep's 2010 Instructor of the Year, Matt Douglas for GMATT Mondays

Visit the Veritas Prep Blog

Try the FREE Veritas Prep Practice Test
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 768
Joined: Wed Dec 28, 2011 4:18 pm
Location: Berkeley, CA
Thanked: 387 times
Followed by:140 members

by Mike@Magoosh » Fri Feb 14, 2014 8:10 pm
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?
Image
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 :-)
Magoosh GMAT Instructor
https://gmat.magoosh.com/
Top
Senior | Next Rank: 100 Posts
Posts: 74
Joined: Fri May 11, 2012 9:06 pm

by parulmahajan89 » Sun Feb 16, 2014 7:32 pm
Thank you. I am sorry I could not post the diagram before.

Can you just tell by looking at the diagram that triangles are prop?

Also is there any other way to solve this question?

Thanks
parul
Top
Post new topic Post Reply
• Page 1 of 1