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

Attachment:

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
_________________

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 = 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 !!
_________________

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

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22 Mar 2015, 06:12

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

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17 Apr 2016, 01:28

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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

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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

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

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

Show Tags

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 = 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

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.
_________________

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
_________________

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

Show Tags

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?

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

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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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