AMC 12 2004a Problem 8

In the overlapping triangles $\triangle{ABC}$ and $\triangle{ABE}$ sharing common side $AB$, $\angle{EAB}$ and $\angle{ABC}$ are right angles, $AB=4$, $BC=6$, $AE=8$, and $\overline{AC}$ and $\overline{BE}$ intersect at $D$. What is the difference between the areas of $\triangle{ADE}$ and $\triangle{BDC}$?

$\text{(A) } 2 \text{(B) } 4 \text{(C) } 5 \text{(D) } 8 \text{(E) } 9$

size(150);
defaultpen(linewidth(0.4));
//Variable Declarations
pair A, B, C, D, E;

//Variable Definitions
A=(0, 0);
B=(4, 0);
C=(4, 6);
E=(0, 8);
D=extension(A,C,B,E);

//Initial Diagram
draw(A--B--C--A--E--B);
label("$A$",A,SW);
label("$B$",B,SE);
label("$C$",C,NE);
label("$D$",D,3N);
label("$E$",E,NW);

//Side labels
label("$4$",A--B,S);
label("$8$",A--E,W);
label("$6$",B--C,ENE);