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

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by AAPL » Mon Sep 10, 2018 5:30 am

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B

C

D

E

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Magoosh

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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

OA B.
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by Brent@GMATPrepNow » Mon Sep 10, 2018 7:27 am
AAPL wrote:Magoosh

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

OA B.
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
Brent Hanneson - Creator of GMATPrepNow.com
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In the figure, ABCD is a square, and all the dots are

by fskilnik@GMATH » Mon Sep 10, 2018 10:34 am
Hi, Brent!

Your solution is beautiful, mathematically and graphically speaking!

Got a well-deserved "+1 upvote post" from me!

Regards
fskilnik.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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by Brent@GMATPrepNow » Mon Sep 10, 2018 3:28 pm
Thanks Fabio!
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