1. An area identifying device comprising: a projecting unit configured to project a pattern so that the pattern performs a predetermined movement; an image capturing unit configured to capture, in time-sequential order, images of projection areas on which the pattern is projected; and a processor configured to execute a program to implement a calculating unit and an identifying unit, the calculating unit being configured to calculate, based on pixel values of the images, an amount of change of pattern appearances for each of multiple image areas in the images, and the identifying unit being configured to identify, as a spatial location of a reflective area of a physical item that has a constant reflectance ratio, at least one image area having a different amount of change of the pattern appearances from a reference amount of change of the pattern appearances based on the predetermined movement, among the calculated amounts of change of the pattern appearances.