GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 12 Nov 2018, 10:01

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.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • Essential GMAT Time-Management Hacks

     November 14, 2018

     November 14, 2018

     08:00 PM MST

     09:00 PM MST

    Join the webinar and learn time-management tactics that will guarantee you answer all questions, in all sections, on time. Save your spot today! Nov. 14th at 7 PM PST
  • $450 Tuition Credit & Official CAT Packs FREE

     November 15, 2018

     November 15, 2018

     10:00 PM MST

     11:00 PM MST

    EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299)

The height of isosceles trapezoid ABDC is 12 units. The

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Senior Manager
Senior Manager
avatar
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 475
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
The height of isosceles trapezoid ABDC is 12 units. The  [#permalink]

Show Tags

New post 07 Feb 2012, 16:02
2
14
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

66% (01:47) correct 34% (01:46) wrong based on 399 sessions

HideShow timer Statistics

Attachment:
Trapezoid ABCD.PNG
Trapezoid ABCD.PNG [ 4.37 KiB | Viewed 26063 times ]
The height of isosceles trapezoid ABDC is 12 units. The length of diagonal AD is 15 units. What is the area of trapezoid ABDC?

(A) 72
(B) 90
(C) 96
(D) 108
(E) 180

_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50543
Re: Area of Trapezoid ABCD?  [#permalink]

Show Tags

New post 07 Feb 2012, 16:22
10
8
The height of isosceles trapezoid ABDC is 12 units. The length of diagonal AD is 15 units. What is the area of trapezoid ABDC?
(A) 72
(B) 90
(C) 96
(D) 108
(E) 180
Attachment:
Trapezoid-area.PNG
Trapezoid-area.PNG [ 5.88 KiB | Viewed 32226 times ]
ED^2+AE^2=AD^2 -->ED^2+12^2=15^2 --> ED=9. Now, as the trapezoid isosceles then CE=FD=x --> AB=9-x and CD=9+x.

Area of trapezoid \(are=a*\frac{b_1+b_2}{2}\), where b1, b2 are the lengths of the two bases a is the altitude of the trapezoid. Hence, the are of trapezoid ABCD is \(area=AE*\frac{AB+CD}{2}=12*\frac{(9-x)+(9+x)}{2}=12*9=108\).

Answer: D.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

General Discussion
Senior Manager
Senior Manager
avatar
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 475
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Re: Area of Trapezoid ABCD?  [#permalink]

Show Tags

New post 07 Feb 2012, 16:06
Sorry guys - I should have said how I am trying to solve.

I draw the two perpendiculars from vertex A and B and called them E and F. So that I have a rectangle called ABEF. Now as we know its an isosceles trapezoid AC = BD and therefore angle C is equal to angle D. Height is 12 and diagonal is 15. Therefore, ED = 9. But, I am struggling to find CE and FD? Can someone please help?
_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

Senior Manager
Senior Manager
avatar
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 475
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Re: Area of Trapezoid ABCD?  [#permalink]

Show Tags

New post 07 Feb 2012, 16:26
Bunuel - thanks. I think there is a typo in our explanation. Do you mean CE = FD = x?

Also, how come they will be equal? Even if this is an isosceles trapezoid then also AC = BD, or am I not getting it right.
_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50543
The height of isosceles trapezoid ABDC is 12 units. The  [#permalink]

Show Tags

New post 07 Feb 2012, 16:31
1
3
enigma123 wrote:
Bunuel - thanks. I think there is a typo in our explanation. Do you mean CE = FD = x?

Also, how come they will be equal? Even if this is an isosceles trapezoid then also AC = BD, or am I not getting it right.


Image
Triangles CAE and DBF are congruent: AC=BD, AE=BF=altitude, <ACE=<BDF, <AEC=<BFD=90, ... --> CE = FD = x.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Senior Manager
Senior Manager
avatar
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 475
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Re: Area of Trapezoid ABCD?  [#permalink]

Show Tags

New post 07 Feb 2012, 16:35
1
Many thanks Bunuel. All makes sense now to me.
_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

Manager
Manager
avatar
Joined: 27 Feb 2012
Posts: 121
Re: The height of isosceles trapezoid ABDC is 12 units. The  [#permalink]

Show Tags

New post 25 May 2013, 13:14
3
enigma123 wrote:
The height of isosceles trapezoid ABDC is 12 units. The length of diagonal AD is 15 units. What is the area of trapezoid ABDC?

(A) 72
(B) 90
(C) 96
(D) 108
(E) 180


Another approach....Imagine this as the one attached below and then find the area of rectangle.
12*9 = 108

Attachment:
Symmetry.jpg
Symmetry.jpg [ 23.87 KiB | Viewed 24216 times ]

_________________

---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Please +1 KUDO if my post helps. Thank you.

SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1749
Concentration: Finance
GMAT ToolKit User
Re: The height of isosceles trapezoid ABDC is 12 units. The  [#permalink]

Show Tags

New post 05 Feb 2014, 14:29
enigma123 wrote:
Attachment:
Trapezoid ABCD.PNG
The height of isosceles trapezoid ABDC is 12 units. The length of diagonal AD is 15 units. What is the area of trapezoid ABDC?

(A) 72
(B) 90
(C) 96
(D) 108
(E) 180


Tricky problem +1

It's going to be a bit hard to explain without an image but I'll give my best shot

Isosceles trapezoid is key

So the area is the average of the bases * height

Height is 12

So we have that the triangle with hypotenuse 15 and height 12 have a base of 9. Likewise the other triangle will have the same base of 9 since it is a mirror image given that trapezoid is isosceles

Now we don't know what the smaller base is but check this out:

Let's give X to the small base and y to the other two measurements that complete the larger base

So small base : x
Large base: 2y + x

Now, we also know that x + y = 9

So the average of both bases will be : 2x + 2y = 18 / 2 = 9

So area is 9 * 12 = 108

Answer is D

Hope it clarifies
Cheers
J
Intern
Intern
avatar
Joined: 15 Jul 2012
Posts: 34
GMAT ToolKit User
Re: The height of isosceles trapezoid ABDC is 12 units. The  [#permalink]

Show Tags

New post 24 Jun 2014, 06:59
Bunuel wrote:
enigma123 wrote:
Bunuel - thanks. I think there is a typo in our explanation. Do you mean CE = FD = x?

Also, how come they will be equal? Even if this is an isosceles trapezoid then also AC = BD, or am I not getting it right.


Triangles CAE and DBF are congruent: AC=BD, AE=BF=altitude, <ACE=<BDF, <AEC=<BFD=90, ... --> CE = FD = x.


can you please explain the colored part? how are these 2 angles equal
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50543
Re: The height of isosceles trapezoid ABDC is 12 units. The  [#permalink]

Show Tags

New post 24 Jun 2014, 07:15
saggii27 wrote:
Bunuel wrote:
enigma123 wrote:
Bunuel - thanks. I think there is a typo in our explanation. Do you mean CE = FD = x?

Also, how come they will be equal? Even if this is an isosceles trapezoid then also AC = BD, or am I not getting it right.


Triangles CAE and DBF are congruent: AC=BD, AE=BF=altitude, <ACE=<BDF, <AEC=<BFD=90, ... --> CE = FD = x.


can you please explain the colored part? how are these 2 angles equal


Because triangles CAE and DBF are congruent, the angles there are also congruent.

Generally, in isosceles trapezoid the base angles have the same measure.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
B
Joined: 10 Mar 2014
Posts: 198
Premium Member
The height of isosceles trapezoid ABDC is 12 units. The  [#permalink]

Show Tags

New post 01 Aug 2014, 06:39
Bunuel wrote:
The height of isosceles trapezoid ABDC is 12 units. The length of diagonal AD is 15 units. What is the area of trapezoid ABDC?
(A) 72
(B) 90
(C) 96
(D) 108
(E) 180
Attachment:
Trapezoid-area.PNG
ED^2+AE^2=AD^2 -->ED^2+12^2=15^2 --> ED=9. Now, as the trapezoid isosceles then CE=FD=x --> AB=9-x and CD=9+x.

Area of trapezoid \(are=a*\frac{b_1+b_2}{2}\), where b1, b2 are the lengths of the two bases a is the altitude of the trapezoid. Hence, the are of trapezoid ABCD is \(area=AE*\frac{AB+CD}{2}=12*\frac{(9-x)+(9+x)}{2}=12*9=108\).

Answer: D.


Hi Bunuel,

I have one confusion here.

We say Trapezoid is having one pair of sides parallel and it is known as base of trapezoid so they should have same angle as both are parallel. Now in case of isoceles triangle it is given that base angles are same. So what is difference here for base angles in Trapezoid and isoceles trapozoid.

doubt from question explanation by you
As we say we can cut a trapezoid in one rectangle and two right triangle. so if this is not isoceles trapezoid still CE= FD=x. as both triangle are similar.

Please clarify

Thanks.
Intern
Intern
User avatar
B
Joined: 16 Mar 2014
Posts: 16
GMAT Date: 08-18-2015
GMAT ToolKit User Premium Member Reviews Badge
Re: The height of isosceles trapezoid ABDC is 12 units. The  [#permalink]

Show Tags

New post 06 Oct 2015, 10:03
enigma123 wrote:
Attachment:
The attachment Trapezoid ABCD.PNG is no longer available
The height of isosceles trapezoid ABDC is 12 units. The length of diagonal AD is 15 units. What is the area of trapezoid ABDC?

(A) 72
(B) 90
(C) 96
(D) 108
(E) 180

Hi all,
Here is another approach. Hope it works.
Please see attached image.
BC = AD = 15, EH = BK = 12. In the right triangle AHD, AH^2 + HD^2 = AD^2 => HD = 9.
The area of the right triangle BHD = 0.5 x BK x HD = 0.5 x 12 x 9 = 54.
Similar for the right triangle AKC, S triangle AKC = 54.
We can observe that Area of BHD + Area of AKC = Area of ABDC (the overlapping area of the two triangles is OHK = The area of AOB- the one supplement BHD and AKC to make ABDC) = 54 + 54 = 108.

Hope it clear.
Attachments

geometry.png
geometry.png [ 6.32 KiB | Viewed 18838 times ]

Director
Director
User avatar
G
Joined: 26 Oct 2016
Posts: 641
Location: United States
Concentration: Marketing, International Business
Schools: HBS '19
GMAT 1: 770 Q51 V44
GPA: 4
WE: Education (Education)
Re: The height of isosceles trapezoid ABDC is 12 units. The  [#permalink]

Show Tags

New post 30 Dec 2016, 04:10
1
By sketching a drawing of trapezoid ABDC with the height and diagonal drawn in, we can use the Pythagorean theorem to see the ED = 9. We also know that ABDC is an isosceles trapezoid, meaning that AC = BD; from this we can deduce that CE = FD, a value we will call x. The area of a trapezoid is equal to the average of the two bases multiplied by the height.
The bottom base, CD, is the same as CE + ED, or x + 9. The top base, AB, is the same as ED – FD, or 9 – x.
Thus the average of the two bases is . {(9+x) + (9-x)}/2 = 9
Multiplying this average by the height yields the area of the trapezoid: 9*12 = 108.
Attachments

Area_problem.PNG
Area_problem.PNG [ 12.84 KiB | Viewed 14357 times ]


_________________

Thanks & Regards,
Anaira Mitch

Manager
Manager
User avatar
G
Joined: 15 Dec 2015
Posts: 116
GMAT 1: 660 Q46 V35
GPA: 4
WE: Information Technology (Computer Software)
Re: The height of isosceles trapezoid ABDC is 12 units. The  [#permalink]

Show Tags

New post 03 Aug 2017, 02:14
Bunuel: Can you please provide similar problems.
Manager
Manager
avatar
B
Joined: 02 Jan 2016
Posts: 112
Reviews Badge CAT Tests
Re: The height of isosceles trapezoid ABDC is 12 units. The  [#permalink]

Show Tags

New post 12 Sep 2018, 10:50
I took an educated guess, the height = 12, formula is H* average base, so answer has to be multiple of 12.
The base has to be somewhere around 15 as the hypotnuse is 15. So I selected D. being the highest and "E" was too great
GMAT Club Bot
Re: The height of isosceles trapezoid ABDC is 12 units. The &nbs [#permalink] 12 Sep 2018, 10:50
Display posts from previous: Sort by

The height of isosceles trapezoid ABDC is 12 units. The

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.