Size... what do you mean by size (pixels or scale)?
If your "container" is a UIWidget, you can just call the container and look for height and width property:
Script on container:
float height = this.GetComponent<UIWidget>().height;
float width = this.GetComponent<UIWidget>().width;
However, the widget is not going to change it's dimensions because you created a sprite as it's child.
If your "container" is just an empty GameObject then there is no size except scale, which is found by looking in the property this.transform.scale