So EB 1 is parallel to AB.

Therefore, the distance from point E to the plane is converted into the distance from B 1 to the plane.

Let the midpoint of BC 1 be OB 1 and the vertical BC 1.

So, B 1O is what you want.

B 1O is the root of 2.

So the distance from e to the plane ABC 1D 1 is the root of 2/2.