let each side of the square be a , then area = a x a

New side = 125a / 100 = 5a / 4

New area =$\left(5a \times 5a\right)$ / $\left(4 \times 4\right)$ = (25a²/16) 

increased area== (25a²/16) - a²

Increase %= [(9a²/16 ) x (1/a² ) x 100]% = 56.25%