Last visit was: 28 Apr 2026, 05:52 It is currently 28 Apr 2026, 05:52
Home
Messages
Tests
Schools
Events
Close
GMAT Club Daily Prep
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
505-555 (Easy)|   Geometry|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 28 Apr 2026
Posts: 109,948
Own Kudos:
811,698
 [5]
Given Kudos: 105,927
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,948
Kudos: 811,698
 [5]
ABCD is a quadrilateral, with AB parallel to CD (see figure). E is a p 01 Jul 2015, 03:01
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

15% (low)

Question Stats:

85% (02:09) correct 15% (02:23) wrong based on 295 sessions

History

Date
Time
Result
Not Attempted Yet

ABCD is a quadrilateral, with AB parallel to CD (see figure). E is a point between C and D such that AE represents the height of ABCD, and E is the midpoint of CD. If AB is 4 inches long, AE is 5 inches long, and the area of triangle AED is 12.5 square inches, what is the area of ABCD? (Note: figure not drawn to scale.)

A. 30 inches
B. 35 inches
C. 40 inches
D. 45 inches
E. 50 inches

Kudos for a correct solution.

Show Spoiler
Attachment:
2015-07-01_1359.png
2015-07-01_1359.png [ 5.02 KiB | Viewed 12491 times ]
ShowHide Answer
Official Answer
B
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 27 Apr 2026
Posts: 11,231
Own Kudos:
45,034
 [1]
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,231
Kudos: 45,034
 [1]
ABCD is a quadrilateral, with AB parallel to CD (see figure). E is a p 01 Jul 2015, 03:40
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

ABCD is a quadrilateral, with AB parallel to CD (see figure). E is a point between C and D such that AE represents the height of ABCD, and E is the midpoint of CD. If AB is 4 inches long, AE is 5 inches long, and the area of triangle AED is 12.5 square inches, what is the area of ABCD? (Note: figure not drawn to scale.)

A. 30 inches
B. 35 inches
C. 40 inches
D. 45 inches
E. 50 inches

Kudos for a correct solution.

Show Spoiler
Attachment:
2015-07-01_1359.png
Show more

lets see the area first .. AE is 5 inches long, and the area of triangle AED is 12.5 square inches.. (1/2)*5*DE=12.5
so DE=5.. as E is the mid point CD=10..
now AB ll CD ..
so it is a trapezium with LLel sides 10 and 4 with height 5..
area of ABCD =(10+4)*5/2=35..
ans B
User avatar
GMATinsight
User avatar
Major Poster
Joined: 08 Jul 2010
Last visit: 26 Apr 2026
Posts: 6,979
Own Kudos:
16,929
 [3]
Given Kudos: 128
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Products:
My Reviews
Expert
Expert reply
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
Posts: 6,979
Kudos: 16,929
 [3]
ABCD is a quadrilateral, with AB parallel to CD (see figure). E is a p 01 Jul 2015, 04:13
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel

ABCD is a quadrilateral, with AB parallel to CD (see figure). E is a point between C and D such that AE represents the height of ABCD, and E is the midpoint of CD. If AB is 4 inches long, AE is 5 inches long, and the area of triangle AED is 12.5 square inches, what is the area of ABCD? (Note: figure not drawn to scale.)

A. 30 inches
B. 35 inches
C. 40 inches
D. 45 inches
E. 50 inches

Kudos for a correct solution.

Show Spoiler
Attachment:
The attachment 2015-07-01_1359.png is no longer available
Show more


Draw the figure for every geometry question

Answer: Option B
Attachments

File comment: www.GMATinsight.com
Solution 1212.jpg
Solution 1212.jpg [ 131.12 KiB | Viewed 10767 times ]

User avatar
balamoon
User avatar
Joined: 26 Dec 2011
Last visit: 04 May 2025
Posts: 111
Own Kudos:
313
 [1]
Given Kudos: 91
Schools: HBS '18 IIMA
Schools: HBS '18 IIMA
Posts: 111
Kudos: 313
 [1]
ABCD is a quadrilateral, with AB parallel to CD (see figure). E is a p 01 Jul 2015, 07:03
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

ABCD is a quadrilateral, with AB parallel to CD (see figure). E is a point between C and D such that AE represents the height of ABCD, and E is the midpoint of CD. If AB is 4 inches long, AE is 5 inches long, and the area of triangle AED is 12.5 square inches, what is the area of ABCD? (Note: figure not drawn to scale.)

A. 30 inches
B. 35 inches
C. 40 inches
D. 45 inches
E. 50 inches

Kudos for a correct solution.

Show Spoiler
Attachment:
2015-07-01_1359.png
Show more

Solution -

Area of AED = 1/2(DE*AE) -> 12.5 = 0.5 (DE*5) -> DE = 5.
E is the mid point, so DE = EC =5.

Area of quadrilateral ABCD = 1/2(DC+AB)*AE = 0.5*(10+4)*5 = 35 inches^2.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 28 Apr 2026
Posts: 109,948
Own Kudos:
811,698
Given Kudos: 105,927
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,948
Kudos: 811,698
ABCD is a quadrilateral, with AB parallel to CD (see figure). E is a p 06 Jul 2015, 02:45
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

ABCD is a quadrilateral, with AB parallel to CD (see figure). E is a point between C and D such that AE represents the height of ABCD, and E is the midpoint of CD. If AB is 4 inches long, AE is 5 inches long, and the area of triangle AED is 12.5 square inches, what is the area of ABCD? (Note: figure not drawn to scale.)

A. 30 inches
B. 35 inches
C. 40 inches
D. 45 inches
E. 50 inches

Kudos for a correct solution.

Show Spoiler
Attachment:
2015-07-01_1359.png
Show more

MANHATTAN GMAT OFFICIAL SOLUTION:

If E is the midpoint of C, then CE = DE = x. You can determine the length of x by using what you know about the area of triangle AED:

A = (b*h)/2;
12.5 = 5x/2;
x = 5.

Therefore, the length of CD is 2x, or 10.

To find the area of the trapezoid, use the formula:
\(A=\frac{b_1+b_2}{2}*h=\frac{4+10}{2}*5=35\) in^2.

Answer: B.
avatar
asfandkhan
avatar
Joined: 17 Mar 2019
Last visit: 01 May 2024
Posts: 3
Given Kudos: 2
Posts: 3
Kudos: 0
ABCD is a quadrilateral, with AB parallel to CD (see figure). E is a p 14 Jun 2019, 11:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello,

I tried solving the problem in a slightly different way and ended up getting a different answer. There is obviously a gap in my understanding so would really appreciate if someone could point that out. Here was my thought process:

Since AB=4 and CE=AB, where is E is the midpoint of CD, wouldn't CD=2AB or 2CE or 2*4=8?

Area= (4+8)*5/2=30

Thanks again,
Asfand
avatar
tittoo
avatar
Joined: 15 Feb 2017
Last visit: 09 Nov 2020
Posts: 61
Own Kudos:
34
Given Kudos: 59
Posts: 61
Kudos: 34
ABCD is a quadrilateral, with AB parallel to CD (see figure). E is a p 03 Aug 2020, 15:58
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If we are not given that E is a midpoint, how can we solve this via decomposition?
I tried solving for the area of the triangle on the left, the rectangle in the middle but got stuck with the area of the triangle on the right.

How to solve for the area of the triangle on the right?
I have the height as 5 but not the base.

Thanks!
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,987
Own Kudos:
1,119
Posts: 38,987
Kudos: 1,119
ABCD is a quadrilateral, with AB parallel to CD (see figure). E is a p 26 Oct 2023, 19:49
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109948 posts
Krunaal
Tuck School Moderator
852 posts