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Senior Manager  Status: Do and Die!!
Joined: 15 Sep 2010
Posts: 253
If ABCD is a square with area 625, and CEFD is a rhombus wit  [#permalink]

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2
38 00:00

Difficulty:   95% (hard)

Question Stats: 38% (02:40) correct 63% (02:34) wrong based on 272 sessions

### HideShow timer Statistics Attachment: rumbs.JPG [ 3.74 KiB | Viewed 21077 times ]
If ABCD is a square with area 625, and CEFD is a rhombus with area 500, then the area of the shaded region is

A. 125
B. 175
C. 200
D. 250
E. 275

_________________
I'm the Dumbest of All !!
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 9446
Location: Pune, India

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15
6
Area of shaded region = Area of square - (Area of rhombus - Area of triangle MFD)

Attachment: Ques2.jpg [ 8.55 KiB | Viewed 21077 times ]

Area of square = 625 so side = 25
Area of rhombus = 500. So altitude = 500/25 = 20
MF = root (25^2 - 20^2) = 15
Area of triangle MFD = (1/2) * 15 * 20 = 150

Area of shaded region = 625 - (500 - 150) = 275
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Karishma
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Manager  Joined: 17 Sep 2010
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Concentration: General Management, Finance
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Nice explanation.

VeritasPrepKarishma wrote:
Area of shaded region = Area of square - (Area of rhombus - Area of triangle MFD)

Attachment:
Ques2.jpg

Area of square = 625 so side = 25
Area of rhombus = 500. So altitude = 500/25 = 20
MF = root (25^2 - 20^2) = 15
Area of triangle MFD = (1/2) * 15 * 20 = 150

Area of shaded region = 625 - (500 - 150) = 275
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Posts: 836
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GMAT 1: 760 Q49 V44 GPA: 3.88
WE: Engineering (Computer Software)

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VeritasPrepKarishma wrote:
Area of shaded region = Area of square - (Area of rhombus - Area of triangle MFD)

Attachment:
Ques2.jpg

Area of square = 625 so side = 25
Area of rhombus = 500. So altitude = 500/25 = 20
MF = root (25^2 - 20^2) = 15
Area of triangle MFD = (1/2) * 15 * 20 = 150

Area of shaded region = 625 - (500 - 150) = 275

Kudos to Karishma. Failed to apply some basic theorems.

Went to calculation of diagonals of rhombus GMAT questions are lot easier than you think !!
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GMAT 1: 650 Q43 V37 GRE 1: Q157 V158 GPA: 2.66
Re: If ABCD is a square with area 625, and CEFD is a rhombus wit  [#permalink]

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VeritasPrepKarishma wrote:
Area of shaded region = Area of square - (Area of rhombus - Area of triangle MFD)

Attachment:
Ques2.jpg

Area of square = 625 so side = 25
Area of rhombus = 500. So altitude = 500/25 = 20
MF = root (25^2 - 20^2) = 15
Area of triangle MFD = (1/2) * 15 * 20 = 150

Area of shaded region = 625 - (500 - 150) = 275

VeritasPrepKarishma

The only thing that threw me off in this problem is the fact that when I read, on a different website, it said that the figure is not drawn to scale? I had initially made the assumption that the base of the rhombus was equal to the length of the square and derived the height using that- but then I second guessed myself and try to work backwards from the area of the rhombus in order to find the lengths of the diagonals and found myself in a mess. In this problem we can make the assumption that the base of the rhombus is equal to a side length of the square? That seems to be a valid takeaway from initially glancing at the problem
Manager  B
Joined: 07 Jun 2017
Posts: 100
Re: If ABCD is a square with area 625, and CEFD is a rhombus wit  [#permalink]

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VeritasPrepKarishma wrote:
Area of shaded region = Area of square - (Area of rhombus - Area of triangle MFD)

Attachment:
Ques2.jpg

Area of square = 625 so side = 25
Area of rhombus = 500. So altitude = 500/25 = 20
MF = root (25^2 - 20^2) = 15
Area of triangle MFD = (1/2) * 15 * 20 = 150

Area of shaded region = 625 - (500 - 150) = 275

Dear Karishma,

how do you get "MF = root (25^2 - 20^2) = 15"?
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Re: If ABCD is a square with area 625, and CEFD is a rhombus wit  [#permalink]

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Nunuboy1994 wrote:
VeritasPrepKarishma wrote:
Area of shaded region = Area of square - (Area of rhombus - Area of triangle MFD)

Attachment:
Ques2.jpg

Area of square = 625 so side = 25
Area of rhombus = 500. So altitude = 500/25 = 20
MF = root (25^2 - 20^2) = 15
Area of triangle MFD = (1/2) * 15 * 20 = 150

Area of shaded region = 625 - (500 - 150) = 275

VeritasPrepKarishma

The only thing that threw me off in this problem is the fact that when I read, on a different website, it said that the figure is not drawn to scale? I had initially made the assumption that the base of the rhombus was equal to the length of the square and derived the height using that- but then I second guessed myself and try to work backwards from the area of the rhombus in order to find the lengths of the diagonals and found myself in a mess. In this problem we can make the assumption that the base of the rhombus is equal to a side length of the square? That seems to be a valid takeaway from initially glancing at the problem

It is not an assumption from the figure. You are given that ABCD is a square so CD is a side of the square. You are also given that CEFD is a rhombus so CD is a side of the rhombus too. Hence the base of the rhombus is equal to the length of the side of the square.
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Re: If ABCD is a square with area 625, and CEFD is a rhombus wit  [#permalink]

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1
pclawong wrote:
VeritasPrepKarishma wrote:
Area of shaded region = Area of square - (Area of rhombus - Area of triangle MFD)

Attachment:
Ques2.jpg

Area of square = 625 so side = 25
Area of rhombus = 500. So altitude = 500/25 = 20
MF = root (25^2 - 20^2) = 15
Area of triangle MFD = (1/2) * 15 * 20 = 150

Area of shaded region = 625 - (500 - 150) = 275

Dear Karishma,

how do you get "MF = root (25^2 - 20^2) = 15"?

Area of rhombus is Base*Height = 500
Height = 500/25 = 20 = MD

Now MFD is right angled triangle so using pythagorean theorem,
MD^2 + MF^2 = FD^2
MF^2 = FD^2 - MD^2
MF = sqrt(25^2 - 20^2)
MF = sqrt(625 - 400)
MF = sqrt(225)
Mf = 15
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Karishma
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GMAT 1: 690 Q43 V41 Re: If ABCD is a square with area 625, and CEFD is a rhombus wit  [#permalink]

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VeritasPrepKarishma wrote:
Area of shaded region = Area of square - (Area of rhombus - Area of triangle MFD)

Attachment:
Ques2.jpg

Area of square = 625 so side = 25
Area of rhombus = 500. So altitude = 500/25 = 20
MF = root (25^2 - 20^2) = 15
Area of triangle MFD = (1/2) * 15 * 20 = 150

Area of shaded region = 625 - (500 - 150) = 275

I don't understand. Is there a different perspective with which we are looking at the diagram in this solution? The one in question is from a different angle, right?
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Re: If ABCD is a square with area 625, and CEFD is a rhombus wit  [#permalink]

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shrive555 wrote:
Attachment:
rumbs.JPG
If ABCD is a square with area 625, and CEFD is a rhombus with area 500, then the area of the shaded region is

A. 125
B. 175
C. 200
D. 250
E. 275

The area of the rhombus is given by base*height
Since area =500=25*h therefore h=20
now we can find the hypotenuse of the triangle =15
area of the triangle is =150
So 500-150=350
The area of the shaded region =625-350=
275
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Re: If ABCD is a square with area 625, and CEFD is a rhombus wit  [#permalink]

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VeritasPrepKarishma wrote:
Area of shaded region = Area of square - (Area of rhombus - Area of triangle MFD)

Attachment:
Ques2.jpg

Area of square = 625 so side = 25
Area of rhombus = 500. So altitude = 500/25 = 20
MF = root (25^2 - 20^2) = 15
Area of triangle MFD = (1/2) * 15 * 20 = 150

Area of shaded region = 625 - (500 - 150) = 275

Hi Karishma

Can you please tell How did we arrive at FD=25 ?

Thank you
Senior Manager  G
Status: love the club...
Joined: 24 Mar 2015
Posts: 275
If ABCD is a square with area 625, and CEFD is a rhombus wit  [#permalink]

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VeritasPrepKarishma wrote:
Area of shaded region = Area of square - (Area of rhombus - Area of triangle MFD)

Attachment:
Ques2.jpg

Area of square = 625 so side = 25
Area of rhombus = 500. So altitude = 500/25 = 20
MF = root (25^2 - 20^2) = 15
Area of triangle MFD = (1/2) * 15 * 20 = 150

Area of shaded region = 625 - (500 - 150) = 275

Hi Karishma

Can you please tell How did we arrive at FD=25 ?

Thank you

hi

I am not Karishma mam the great, but I will try to help you

please remember that the sides of a rhombus are always equal
here you can see the side "CD", which is a side of both the square and the rhombus

so, as the side of the square is 25, the side of the rhombus is also 25

hope this helps!

thanks Non-Human User Joined: 09 Sep 2013
Posts: 11706
Re: If ABCD is a square with area 625, and CEFD is a rhombus wit  [#permalink]

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