0.25 is super complicated. If you don't want to be a top student, you don't have to meet.

Let the side length be a.

Triangle dcf is equal to triangle bce.

Triangle deg is similar to triangle bce and triangle dcf.

Angle dge= angle dcf=90 degrees-triangle dbf is an isosceles triangle.

So bd=bf dg=gf

Because bd= root number 2a; Bc=a, so ce= root number 2-1a.

Triangle dge is similar to triangle bgf.

So ge: gf = DG: GB

Cross multiply dg squared = ge GB = 4-2 times the root number 2.

Pythagorean theorem 4*dg square (that is, df square) =dc square +cf square =4-2 times the root sign and 2 times A square.

1/4 = one square divided by two formulas.

That is, the square area is 0.25.