Note that triangle BYX is similar to triangle BCA
AC = BC = 12 + 6 = 18
BA = sqrt (18^2 + 18^2) = sqrt (2 *18^2) = 18 sqrt (2)
Scale factor of BYX to BCA = 12/ (18 sqrt (2)) = 2/ (3 sqrt (2)) = sqrt (2) / 3
Ratio of area of BYX to BCA = (scale factor)^2 = 2/9
Just as QM found !!!!