Since the lines meet the edges of the square at the midpoints, we can divide the square into pairs of triangles with identical areas as below.

From the puzzle a+b=33, c+d=39, therefore the entire square, 2(a+b+c+d)=144, so the square is 12x12 and the base length of each of the eight triangles is 6. Because it is a square we also know that the a and c triangles make up half the area, and the b and d triangles make up the other. So a+c=b+d=36.

With all of this information we can determine the values of the individual areas to be a=12, b=21, c=24, d=15.

Looking only at the areas a and d will pinpoint the coordinates of the interior point (4,5).