Note there are 2 big 45-45-90triangles, 2 small triangles 45-45-90 triangles and a rectangle in the middle.

Thus, the sum of all these areas is the area of big square which is 10x10=100.

The area of the rectange in the middle is 1xX=X

The area of the small triangles can easily be determined because they add up to a perfect square with diagnol of 1, thus the area is 1/2

The area of the big triangles can easily be determined because they add up to a perfect square with diagnol of x thus thee area is (1/2)x^2

Thus we have,

Thus,

Thus,

Thus,