MathDB

Sides

AB,BC,CD

and

DA

of convex polygon

ABCD

have lengths 3,4,12, and 13, respectively, and

\measuredangle CBA

is a right angle. The area of the quadrilateral is
[asy] size(200); defaultpen(linewidth(0.7)+fontsize(10)); real r=degrees((12,5)), s=degrees((3,4)); pair D=origin, A=(13,0), C=D+12*dir(r), B=A+3*dir(180-(90-r+s)); draw(A--B--C--D--cycle); markscalefactor=0.05; draw(rightanglemark(A,B,C)); pair point=incenter(A,C,D); label("

A

", A, dir(point--A)); label("

B

", B, dir(point--B)); label("

C

", C, dir(point--C)); label("

D

", D, dir(point--D)); label("

3

", A--B, dir(A--B)*dir(-90)); label("

4

", B--C, dir(B--C)*dir(-90)); label("

12

", C--D, dir(C--D)*dir(-90)); label("

13

", D--A, dir(D--A)*dir(-90));[/asy]

\text{(A)} \ 32 \qquad \text{(B)} \ 36 \qquad \text{(C)} \ 39 \qquad \text{(D)} \ 42 \qquad \text{(E)} \ 48

Problem Statement