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square geometry

by kobel51 » Wed Jan 15, 2014 7:24 am
Image

In square ABCD above, if DE = EB and DF = FC, then the area of the shaded region is what fraction of the area of square region ABCD?

A) 1/16
B) 1/8
C) 1/6
D) 1/4
E) 1/3
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by Patrick_GMATFix » Wed Jan 15, 2014 7:36 am
The solution below is taken from the GMATFix App.

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by GMATGuruNY » Wed Jan 15, 2014 7:54 am
DE=EB --> E is the CENTER of the square.
DF=FC --> F is the MIDPOINT of CD.
Thus, the square can be divided as follows:
Image
The figure shows that ∆DEF is 1 of 8 congruent triangles.
Thus, ∆DEF is 1/8 of the square.

The correct answer is B.
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