Convex quadrilateral ABCD has AB=3,BC=4,CD=13,AD=12, and ∠ABC=90∘, as shown. What is the area of the quadrilateral?[asy]
unitsize(.4cm);
defaultpen(linewidth(.8pt)+fontsize(14pt));
dotfactor=2;
pair A,B,C,D;
C = (0,0);
B = (0,4);
A = (3,4);
D = (12.8,-2.8);
draw(C--B--A--D--cycle);
draw(rightanglemark(C,B,A,20));
dot("A",A,N);
dot("B",B,NW);
dot("C",C,SW);
dot("D",D,E);
[/asy]<spanclass=′latex−bold′>(A)</span>30<spanclass=′latex−bold′>(B)</span>36<spanclass=′latex−bold′>(C)</span>40<spanclass=′latex−bold′>(D)</span>48<spanclass=′latex−bold′>(E)</span>58.5