MathDB

In rectangle

ADEH

, points

B

and

C

trisect

\overline{AD}

, and points

G

and

F

trisect

\overline{HE}

. In addition, AH \equal{} AC \equal{} 2. What is the area of quadrilateral

WXYZ

shown in the figure?
[asy]defaultpen(linewidth(0.7));pointpen=black; pathpen=black; size(7cm); pair A,B,C,D,E,F,G,H,W,X,Y,Z; A=(0,2); B=(1,2); C=(2,2); D=(3,2); H=(0,0); G=(1,0); F=(2,0); E=(3,0); D('A',A, N); D('B',B,N); D('C',C,N); D('D',D,N); D('E',E,NE); D('F',F,NE); D('G',G,NW); D('H',H,NW); D(A--F); D(B--E); D(D--G); D(C--H); Z=IP(A--F, C--H); Y=IP(A--F, D--G); X=IP(B--E,D--G); W=IP(B--E,C--H); D('W',W,N); D('X',X,plain.E); D('Y',Y,S); D('Z',Z,plain.W); D(A--D--E--H--cycle);[/asy]

<span class='latex-bold'>(A) </span> \frac 12 \qquad <span class='latex-bold'>(B) </span> \frac {\sqrt {2}}2\qquad <span class='latex-bold'>(C) </span> \frac {\sqrt {3}}2 \qquad <span class='latex-bold'>(D) </span> \frac {2\sqrt {2}}3 \qquad <span class='latex-bold'>(E) </span> \frac {2\sqrt {3}}3

Problem Statement