Three circular arcs of radius 5 units bound the region shown. Arcs $AB$ and $AD$ are quarter-circles, and arc $BCD$ is a semicircle. What is the area, in square units, of the region? [asy]
/* AMC8 2000 #19 Problem */
draw((0,0)..(1,1)..(2,0));
draw((0,0)..(.7,-.3)..(1,-1));
draw((1,-1)..(1.3, -0.3)..(2,0));
label("$A$", (1,-1), SW);
label("$B$", (0,0), W);
label("$C$", (1,1),N);
label("$D$", (2,0),E);
[/asy]
Slide I into III and II into IV as indicated by the arrows to create the $5\times 10$ rectangle, which has area $\boxed{50}.$ [asy]
/* AMC8 2000 #19 Solution (only 1 needed - 2nd provided) */
draw((0,0)..(1,1)..(2,0));
draw((0,0)..(.7,-.3)..(1,-1));
draw((1,-1)..(1.3, -0.3)..(2,0));
draw((0,0)--(0,-1)--(2,-1)--(2,0));
draw((.6,.4)--(1.5,-0.5),EndArrow);
draw((1.4,.4)--(.5,-0.5),EndArrow);
draw((0,0)--(2,0),linetype("4 4"));
draw((1,1)--(1,-1),linetype("4 4"));
label("I", (.5,.5));
label("II", (1.5,.5));
label("IV", (0.4, -0.6));
label("III", (1.6, -0.6));
[/asy]