Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: Trapezium area [#permalink]
28 Aug 2010, 10:10

Expert's post

jananijayakumar wrote:

If BE CD, and BC = AB = 3, AE = 4 and CD = 10, what is the area of trapezoid BEDC? (Figure attached) A) 12 B) 18 C) 24 D) 30 E) 48

Attachment:

Untitled.jpg

I guess it's BE||CD (BE is parallel to CD).

Triangles ABE and ACD are similar (they share the same angle CAD and also as BE is parallel to CD then angles by BE and CD are equal, so all 3 angles of these triangles are equal so they are similar triangles).

Property of similar triangles: ratio of corresponding sides are the same: \frac{AB}{AC}=\frac{BE}{CD} --> \frac{3}{6}=\frac{BE}{10} --> BE=5 and AD=2AE=8.

So in triangle ABE sides are AB=3, AE=4 and BE=5: we have 3-4-5 right triangle ABE (with right angle CAD, as hypotenuse is BE=5) and 6-8-10 right angle triangle ACD.

Now, the area_{BEDC}=area_{ACD}-area_{ABE} --> area_{BEDC}=\frac{6*8}{2}-\frac{3*4}{2}=18.

Re: Trapezium area [#permalink]
28 Aug 2010, 11:30

Bunuel - In this case it turned out to be a rt angled triangle so the area calc was easy.. Lets say the bigger triangle were 5 7 9 in sides and the smaller was correspondingly half in size inside of it.. In that case, what would be the easiest way to calculate the trapezium area.. I guess does GMAT require us to remember the formula of the area of a triangle (not the .5 base height) but the one with the sides? Is there an easy way to calculate the area where the sides are given for any triangle? _________________

Re: Trapezium area [#permalink]
28 Aug 2010, 11:48

Expert's post

mainhoon wrote:

Bunuel - In this case it turned out to be a rt angled triangle so the area calc was easy.. Lets say the bigger triangle were 5 7 9 in sides and the smaller was correspondingly half in size inside of it.. In that case, what would be the easiest way to calculate the trapezium area.. I guess does GMAT require us to remember the formula of the area of a triangle (not the .5 base height) but the one with the sides? Is there an easy way to calculate the area where the sides are given for any triangle?

If it were not right triangle we could calculate the area of triangles with Heron's Formula (as we still would knew the lengths of all sides), though I've never seen a GMAT question requiring it. _________________

Re: Trapezium area [#permalink]
13 Sep 2010, 06:18

Bunuel wrote:

jananijayakumar wrote:

If BE CD, and BC = AB = 3, AE = 4 and CD = 10, what is the area of trapezoid BEDC? (Figure attached) A) 12 B) 18 C) 24 D) 30 E) 48

Attachment:

Untitled.jpg

I guess it's BE||CD (BE is parallel to CD).

Triangles ABE and ACD are similar (they share the same angle CAD and also as BE is parallel to CD then angles by BE and CD are equal, so all 3 angles of these triangles are equal so they are similar triangles).

Property of similar triangles: ratio of corresponding sides are the same: \frac{AB}{AC}=\frac{BE}{CD} --> \frac{3}{6}=\frac{BE}{10} --> BE=5 and AD=2AE=8.

So in triangle ABE sides are AB=3, AE=4 and BE=5: we have 3-4-5 right triangle ABE (with right angle CAD, as hypotenuse is BE=5) and 6-8-10 right angle triangle ACD.

Now, the area_{BEDC}=area_{ACD}-area_{ABE} --> area_{BEDC}=\frac{6*8}{2}-\frac{3*4}{2}=18.

Answer: B.

Hope it's clear.

Bunuel... If you say that BC = AB = 3, AE = 4 then how can BE||CD (BE is parallel to CD) true. I am not able to visualize such a figure!!!

Re: Trapezium area [#permalink]
13 Sep 2010, 07:42

Expert's post

utin wrote:

Bunuel wrote:

jananijayakumar wrote:

If BE CD, and BC = AB = 3, AE = 4 and CD = 10, what is the area of trapezoid BEDC? (Figure attached) A) 12 B) 18 C) 24 D) 30 E) 48

Attachment:

Untitled.jpg

I guess it's BE||CD (BE is parallel to CD).

Triangles ABE and ACD are similar (they share the same angle CAD and also as BE is parallel to CD then angles by BE and CD are equal, so all 3 angles of these triangles are equal so they are similar triangles).

Property of similar triangles: ratio of corresponding sides are the same: \frac{AB}{AC}=\frac{BE}{CD} --> \frac{3}{6}=\frac{BE}{10} --> BE=5 and AD=2AE=8.

So in triangle ABE sides are AB=3, AE=4 and BE=5: we have 3-4-5 right triangle ABE (with right angle CAD, as hypotenuse is BE=5) and 6-8-10 right angle triangle ACD.

Now, the area_{BEDC}=area_{ACD}-area_{ABE} --> area_{BEDC}=\frac{6*8}{2}-\frac{3*4}{2}=18.

Answer: B.

Hope it's clear.

Bunuel... If you say that BC = AB = 3, AE = 4 then how can BE||CD (BE is parallel to CD) true. I am not able to visualize such a figure!!!

Why not? Consider triangle CAD, where CA=6 and AD=8. Now draw midsegment BE of a triangle (a line segment joining the midpoints of two sides of a triangle). Properties of a midsegment:

• The midsegment is always parallel to the third side of the triangle. • The midsegment is always half the length of the third side.

Hey everyone, today’s post focuses on the interview process. As I get ready for interviews at Kellogg and Tuck (and TheEngineerMBA ramps up for his HBS... ...

I got invited to interview at Sloan! The date is October 31st. So, with my Kellogg interview scheduled for this Wednesday morning, and my MIT Sloan interview scheduled...