The amount of diagonal tiles can be written as 2x-1 where x is the side length of the square. That means that 2x-1 = 89; x= 45. The area of the square is 45 * 45= 2025. 2025-89 yellow tiles= 1936 gray tiles.
Also, MooMooooMooM answered here first, but this is an explanation as well.