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In the figure, ABCD is a square, and all the dots are evenly

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Bunuel
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In the figure, ABCD is a square, and all the dots are evenly [#permalink] New post   26 Oct 2017, 02:20
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In the figure, ABCD is a square, and all the dots are evenly spaced: each vertical or horizontal distance between two adjacent dots is 3 units. Find the area of the shaded region.

A. 60
B. 72
C. 81
D. 96
E. 120


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Re: In the figure, ABCD is a square, and all the dots are evenly [#permalink] New post   26 Oct 2017, 04:54
Figure missing
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Re: In the figure, ABCD is a square, and all the dots are evenly [#permalink] New post   26 Oct 2017, 23:30
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IlCreatore wrote:
Figure missing


Sorry, added the image. Thank you.
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In the figure, ABCD is a square, and all the dots are evenly [#permalink] New post   27 Oct 2018, 03:47
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GRE - In the figure, ABCD is a square, and all the dots are evenly.jpg
GRE - In the figure, ABCD is a square, and all the dots are evenly.jpg [ 18.37 KiB | Viewed 6886 times ]


In the figure, ABCD is a square, and all the dots are evenly spaced. Each vertical or horizontal distance between two adjacent dots is 3 units. Find the area of the shaded region.

A. 60

B. 72

C. 81

D. 96

E. 120
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AE
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Re: In the figure, ABCD is a square, and all the dots are evenly [#permalink] New post   08 Jan 2019, 19:49
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By close observation all the shaded region fits inside half of the squire.

As each dot to dot is 3 units, each side of the squire is 3*4=12 units.

The area of squire is 12^2=144

The area of the shaded region is 144/2 = 72

Answer. B
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Re: In the figure, ABCD is a square, and all the dots are evenly [#permalink] New post   09 Jan 2019, 06:38
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Carcass wrote:
Attachment:
GRE - In the figure, ABCD is a square, and all the dots are evenly.jpg


In the figure, ABCD is a square, and all the dots are evenly spaced. Each vertical or horizontal distance between two adjacent dots is 3 units. Find the area of the shaded region.

A. 60

B. 72

C. 81

D. 96

E. 120


There are total 4*4 or 16 smaller squares of 3 units..
when we half them, it becomes 16*2=32 right angled triangles..
Now count the number of triangles that are shaded..
1st row - 3, 2nd row-5, 3rd row-5, and 4th row - 3, so total = 3+5+5+3=16..
so 16 out of 32 are shaded that is half of total ..
area = half of 12*12=72
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Re: In the figure, ABCD is a square, and all the dots are evenly [#permalink] New post   09 Jan 2019, 07:21
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Carcass wrote:
Attachment:
The attachment GRE - In the figure, ABCD is a square, and all the dots are evenly.jpg is no longer available


In the figure, ABCD is a square, and all the dots are evenly spaced. Each vertical or horizontal distance between two adjacent dots is 3 units. Find the area of the shaded region.

A. 60

B. 72

C. 81

D. 96

E. 120



Just found the diagram, I believe that is self explanatory.
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Triangles.jpg
Triangles.jpg [ 15.48 KiB | Viewed 6175 times ]

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Re: In the figure, ABCD is a square, and all the dots are evenly [#permalink] New post   10 Jan 2019, 07:20
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pranab01 wrote:
Carcass wrote:
Attachment:
GRE - In the figure, ABCD is a square, and all the dots are evenly.jpg


In the figure, ABCD is a square, and all the dots are evenly spaced. Each vertical or horizontal distance between two adjacent dots is 3 units. Find the area of the shaded region.

A. 60

B. 72

C. 81

D. 96

E. 120



Just found the diagram, I believe that is self explanatory.


Great! That's what I tried to tell in my previous post. Thank you for the diagram and detail explanation.
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Re: In the figure, ABCD is a square, and all the dots are evenly [#permalink] New post   28 Apr 2021, 06:26
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Carcass wrote:
Attachment:
GRE - In the figure, ABCD is a square, and all the dots are evenly.jpg


In the figure, ABCD is a square, and all the dots are evenly spaced. Each vertical or horizontal distance between two adjacent dots is 3 units. Find the area of the shaded region.

A. 60

B. 72

C. 81

D. 96

E. 120

If the vertical or horizontal distance between two adjacent dots is 3 units, then the square has dimensions 12 by 12
So, the area of the ENTIRE SQUARE = (12)(12) = 144

Now, notice that the square is comprised of 32 identical triangles
Image
Since 16 of the triangles are shaded, the shaded regions represent 16/32 (aka 1/2) of the ENTIRE SQUARE

In other words, the area of the shaded region = 1/2 of 144
= 72

Answer: B

Cheers,
Brent
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Re: In the figure, ABCD is a square, and all the dots are evenly [#permalink] New post   28 Feb 2024, 00:24
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