Question 129
For a convex quadrilateral $ABCD$, the conditions $AB = BC = 2$, $CD = 2\sqrt{3}$, $DA = 2\sqrt{5}$ are satisfied. Also, if we let $M$, $N$ be the midpoint of $AC$ and $BD$, respectively, then $MN = \sqrt{2}$. Determine the area of the quadrilateral $ABCD$. Here, by $XY$ we are representing the length of the line segment $XY$.