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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: [#permalink]

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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

[Reveal] Spoiler:
Attachment:
ldvagm_img1.jpg
ldvagm_img1.jpg [ 11.56 KiB | Viewed 784 times ]
[Reveal] Spoiler: OA

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Re: In the figure, ABCD is a square, and all the dots are evenly spaced: [#permalink]

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New post 29 Oct 2017, 04:49
72.. just rearrange the diag to get half the square

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New post 29 Oct 2017, 18:15
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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Re: In the figure, ABCD is a square, and all the dots are evenly spaced: [#permalink]

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New post 29 Oct 2017, 18:28
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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Re: In the figure, ABCD is a square, and all the dots are evenly spaced: [#permalink]

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Bunuel wrote:
Image
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:
Attachment:
The attachment ldvagm_img1.jpg is no longer available

Attachment:
ccccc.jpg
ccccc.jpg [ 26 KiB | Viewed 424 times ]

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

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Re: In the figure, ABCD is a square, and all the dots are evenly spaced: [#permalink]

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New post 31 Oct 2017, 11:59
There are 16 triangles of area 4.5
16*4.5 =72
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Re: In the figure, ABCD is a square, and all the dots are evenly spaced: [#permalink]

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New post 31 Oct 2017, 12:32
I got 72, which is B. All I did was count the triangles. There are probably more efficient ways.
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Re: In the figure, ABCD is a square, and all the dots are evenly spaced: [#permalink]

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New post 01 Nov 2017, 10:20
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
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Re: In the figure, ABCD is a square, and all the dots are evenly spaced:   [#permalink] 01 Nov 2017, 10:20
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In the figure, ABCD is a square, and all the dots are evenly spaced:

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