1980 AHSME Problems/Problem 7
Revision as of 12:10, 16 July 2012 by Mrdavid445 (talk | contribs) (Created page with "==Problem== Sides <math>AB,BC,CD</math> and <math>DA</math> of convex polygon <math>ABCD</math> have lengths 3,4,12, and 13, respectively, and <math>\measuredangle CBA</math> is...")
Problem
Sides 
and 
of convex polygon 
have lengths 3,4,12, and 13, respectively, and 
is a right angle. The area of the quadrilateral is
![[asy] 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]](http://latex.artofproblemsolving.com/0/3/4/03406705488fb5be15f3ce0fda54f0e61223736d.png)
