Household appliance having hinge and hinge for household appliance

The invention relates to a household appliance, in particular a household refrigeration appliance, comprising a body and a closure element which closes a storage space located in the body and is hinged to the body by means of at least one hinge, and the hinge comprising a hinge part on the body side which is fastened to a flat contact surface on the body. The body has positioning elements which are offset with respect to the contact surface in a direction extending perpendicular to the contact surface and which form a form-fitting connection with the hinge part. The invention relates to a hinge for fastening a closure element of a household appliance to a body of the household appliance, comprising a hinge part for fastening to the body, the hinge part having a flat appliance contact surface. A counter-positioning element is formed on the hinge part, said counter-positioning element protruding relative to the appliance contact surface with reference to a direction extending perpendicular to the appliance cont