MathDB

Let

ABCD

be a square, and let

E

and

F

be points on sides

\overline{AB}

and

\overline{CD}

, respectively, such that

AE:EB=AF:FD=2:1

. Let

G

be the intersection of

\overline{AF}

and

\overline{DE}

, and let

H

be the intersection of

\overline{BF}

and

\overline{CE}

. Find the ratio of the area of quadrilateral

EGFH

to the area of square

ABCD

.
[asy] size(5cm,0); draw((0,0)--(3,0)); draw((3,0)--(3,3)); draw((3,3)--(0,3)); draw((0,3)--(0,0)); draw((0,0)--(2,3)); draw((1,0)--(3,3)); draw((0,3)--(1,0)); draw((2,3)--(3,0)); label("

A

",(0,3),NW); label("

B

",(3,3),NE); label("

C

",(3,0),SE); label("

D

",(0,0),SW); label("

E

",(2,3),N); label("

F

",(1,0),S); label("

G

",(0.66666667,1),E); label("

H

",(2.33333333,2),W); [/asy]

Problem Statement