Why the size of transformer decreases if we increases the frequency?

From emf equation of Transformer,

E = 4.44 fNAB 

where E=voltage
f=frequency
A=Area
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.

To decrease the transformer size we will have to some how decrease the power losses … If we change the frequency from 100kHz to 80kHz then there will be a increase in flux density.