Opposite sides of a rhombus are parallel and the same length, therefore the length and orientation of the lower left side of the square are identical to the right hand slope of the triangle with base 18. Similarly the lower right side of the square has the same length and orientation as the left slope of the 38 base triangle. We can now dispense with the rest of the diagram and only look at those two triangles, armed with the knowledge that the angle between them is 90 degrees. This also means that the length of the other two triangle bases was irrelevant, so long as they produced valid triangles.

Dropping perpendicular bisectors from each we get two congruent right angled triangle with legs 9 and 19.

Since the area we seek is simply x^2, we can use Pythagoras to find that the area of the original square is 9^2+19^2, which is equal to 442.