Before any work, other than preparation of the description and the approval, adoption and recording of the same, is done or rights in or ownership of property are acquired by the drainage board, pursuant to any petition filed under section 541, the augmented drainage board shall make a determination, following notice and a hearing as provided in this chapter, which may be the hearing provided for in section 542, as to the public corporations to be assessed for the cost of such work or acquisition. After the hearing and the determination to proceed with such work, the drainage board shall proceed in the same manner as is provided for other drain projects in this chapter and the drainage board shall have the rights and powers so provided.