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

Question

https://gmatclub.com/forum/download/file.php?id=38217 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 ldvagm_img1.jpg

generis · Accepted Answer

ccccc.jpg The dots are evenly spaced; distances between dots are equal. As long as the shapes' side lengths are made with the same number of dots, they are congruent. "Move" some of the shaded parts, see diagram, left square. Right hand square: Now the shaded area is half the square's area. One side of the square = 4 dots * 3 units = 12 Square area = 12 ^2 = 144 Shaded area = half of square = 72 Answer B

AkshatN · Answer

72.. just rearrange the diag to get half the square

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Ayan167 · Answer

B 72
There are six parallelograms with an area of 9 units square each. 
There are four right angled triangles with an area of 4.5 units square each

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laddaboy · Answer

Rearranging blue areas we see that from every single of the 16 sqaures a half portion is coloured. So total coloured sqaures are 8 , hence 9*8 = 72

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arpitj007 · Answer

There are 16 triangles of area 4.5
16*4.5 =72

Plunkster82 · Answer

I got 72, which is B. All I did was count the triangles. There are probably more efficient ways.

NDND · Answer

IMO B

Total area of the square is (3*4)^2= 144
If we counted the number of blue triangles on the left hand-side, we will realize they complete the blue ones on the left hand-side to make half of the total area of the square. Therefore, the shaded area is 144/2 = 72

BrentGMATPrepNow · Answer

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  
 https://i.imgur.com/mHC9rOY.png 
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

bumpbot · Answer

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

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

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