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

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In the figure, ABCD is a square, and all the dots are evenly [#permalink]  27 Oct 2018, 03:47
Expert's post
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Question Stats:

85% (00:44) correct 14% (02:46) wrong based on 7 sessions
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GRE - In the figure, ABCD is a square, and all the dots are evenly.jpg [ 18.37 KiB | Viewed 1890 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
[Reveal] Spoiler: OA

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Re: In the figure, ABCD is a square, and all the dots are evenly [#permalink]  08 Jan 2019, 19:49
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

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Re: In the figure, ABCD is a square, and all the dots are evenly [#permalink]  09 Jan 2019, 06:38
Expert's post
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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Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

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Re: In the figure, ABCD is a square, and all the dots are evenly [#permalink]  09 Jan 2019, 07:21
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.
Attachments

Triangles.jpg [ 15.48 KiB | Viewed 1297 times ]

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Re: In the figure, ABCD is a square, and all the dots are evenly [#permalink]  10 Jan 2019, 07:20
1
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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.
Re: In the figure, ABCD is a square, and all the dots are evenly   [#permalink] 10 Jan 2019, 07:20
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