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In the figure, ABCD is a rectangle and points E, F, G and H are midpoi

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Joined: 02 Sep 2009
Posts: 58428
In the figure, ABCD is a rectangle and points E, F, G and H are midpoi  [#permalink]

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Updated on: 24 Jul 2019, 05:09
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Difficulty:

25% (medium)

Question Stats:

80% (01:16) correct 20% (02:04) wrong based on 15 sessions

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In the figure, ABCD is a rectangle and points E, F, G and H are midpoints of its sides. What is the ratio of the area of the shaded region to the area of the un-shaded region in the rectangle?

(A) 1 : 1
(B) 1 : 2
(C) 2 : 1
(D) 1 : 3
(E) 3 : 1

Source: Nova GMAT
Difficulty Level: 600

Attachment:

2019-04-10_1121.png [ 27.2 KiB | Viewed 378 times ]

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Originally posted by Bunuel on 10 Apr 2019, 00:21.
Last edited by SajjadAhmad on 24 Jul 2019, 05:09, edited 1 time in total.
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Joined: 03 Nov 2018
Posts: 32
Re: In the figure, ABCD is a rectangle and points E, F, G and H are midpoi  [#permalink]

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10 Apr 2019, 01:27
Since E, F, G and H are the midpoints of the sides, EFGH will always be a rhombus.
Area rhombus is diagonal 1 * diagonal 2 / 2, diagonal 1 is equal to 1 side of rectangle ABCD and diagonal 2 to the other side of rectangle ABCD.
This means the area of rhombus EFGH will always be half of the area of rectangle ABCD.
Therefore, the shaded area will also be half.
The ratios of the shaded area to the unshaded area (rhombus) will always be 1 : 1.
A)
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Re: In the figure, ABCD is a rectangle and points E, F, G and H are midpoi  [#permalink]

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10 Apr 2019, 02:38
Bunuel wrote:

In the figure, ABCD is a rectangle and points E, F, G and H are midpoints of its sides. What is the ratio of the area of the shaded region to the area of the un-shaded region in the rectangle?

(A) 1 : 1
(B) 1 : 2
(C) 2 : 1
(D) 1 : 3
(E) 3 : 1

Attachment:
2019-04-10_1121.png

let for rectangle l = 8 and b =6so area = 48
and shaded side gives 4 rectangles area = 1/2 *3*4 *4 = 24
area insided of un shaded part ; base 6 and height 4 ; we have 4 triangles of area total again 24
so ratio ; 24:24 ; 1:1
IMO A
Re: In the figure, ABCD is a rectangle and points E, F, G and H are midpoi   [#permalink] 10 Apr 2019, 02:38
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