A system includes: a projection unit that projects an image on a projection object; an image capturing unit that captures an image of a target object present in an optical path of projection light projected from the projection unit; a detection unit that detects light reflected from the target object, based on a captured image captured by the image capturing unit; a judging unit that judges position information of the target object in target space that corresponds to the image projected by the projection unit, based on the captured image; and an identification unit that identifies a projection area on the projection object in which the image is projected, based on the light reflected from the target object detected by the detection unit and the position information judged by the judging unit.