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If ABCD is a square with area 625, and CEFD is a rhombus wit

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If ABCD is a square with area 625, and CEFD is a rhombus wit [#permalink]

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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
[Reveal] Spoiler: OA

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Re: Rhombus and square [#permalink]

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

Attachment:
Ques2.jpg
Ques2.jpg [ 8.55 KiB | Viewed 12399 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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Re: Rhombus and square [#permalink]

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New post 03 Dec 2010, 13:12
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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Re: Rhombus and square [#permalink]

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New post 19 Jan 2014, 08:41
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 :(

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Re: If ABCD is a square with area 625, and CEFD is a rhombus wit [#permalink]

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Re: If ABCD is a square with area 625, and CEFD is a rhombus wit [#permalink]

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New post 17 Apr 2016, 01:28
Hello from the GMAT Club BumpBot!

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Re: If ABCD is a square with area 625, and CEFD is a rhombus wit [#permalink]

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New post 22 Apr 2017, 17:03
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

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Re: If ABCD is a square with area 625, and CEFD is a rhombus wit [#permalink]

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New post 24 Jul 2017, 09:42
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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New post 24 Jul 2017, 21:56
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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New post 24 Jul 2017, 22:08
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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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Re: If ABCD is a square with area 625, and CEFD is a rhombus wit [#permalink]

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New post 09 Sep 2017, 04:18
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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New post 09 Sep 2017, 06:42
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] 09 Sep 2017, 06:42
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