MathDB

In the figure,

ABCD

is a

2\times 2

square,

E

is the midpoint of

\overline{AD}

, and

F

is on

\overline{BE}

. If

\overline{CF}

is perpendicular to

\overline{BE}

, then the area of quadrilateral

CDEF

is [asy]defaultpen(linewidth(.8pt)); dotfactor=4;
pair A = (0,2); pair B = origin; pair C = (2,0); pair D = (2,2); pair E = midpoint(A--D); pair F = foot(C,B,E);
dot(A);dot(B);dot(C);dot(D);dot(E);dot(F);
label("

A

",A,N);label("

B

",B,S);label("

C

",C,S);label("

D

",D,N);label("

E

",E,N);label("

F

",F,NW);
draw(A--B--C--D--cycle); draw(B--E); draw(C--F); draw(rightanglemark(B,F,C,4));[/asy] (A)\ 2\qquad (B)\ 3 \minus{} \frac {\sqrt {3}}{2}\qquad (C)\ \frac {11}{5}\qquad (D)\ \sqrt {5}\qquad (E)\ \frac {9}{4}

Problem Statement