S diamond =( 1/2)*AC*BD, that is, the area of the diamond is equal to half the product of its diagonal length.

The product of diagonal lengths in your two graphs has changed, and the area of the diamond will definitely change.

Let AO=a and bo = b.

When the side length AB is constant, that is, a*a+b*b is constant, a*b can be changed, for example:

A diamond with a side length of √52,

52=36+ 16=48+4

6*4≠2*4√3