In the diagram, rectangle P Q R S has P S=2 and P Q=4. Points T, U, V, W are positioned so that R T=R U=P W=P V=a. If V U and W T pass through the centre of the rectangle, for what value of a is the shaded region \frac{1}{8} the area of P Q R S ?

Answer Choices
A. \frac{2}{3}
B. \frac{1}{2}
C. \frac{2}{5}
D. \frac{1}{3}
E. \frac{1}{4}