From emf equation of Transformer,
E = 4.44 fNAB
N=number of turns
B=magnetic flux density
In general we can say
A = E/(4.44fNB)
for constant value of E,N,B
if we increase F, then Area of core will decreases means size of transformer will reduce.
At a given power, the total amount of energy that needs to be stored per cycle is inversely related to the frequency (since the higher the frequency, the more cycles per unit time). So, as the frequency goes up, the storage requirement goes down, and therefore the required amount of storage material (e.g., ferrite) goes down as well.