1. A projection system, comprising: a projection unit configured to project a projected image on a surface for projection; an image capturing unit configured to capture an image-capturing area representing an area in which images are capturable and generate a captured image; a configuration information storage unit configured to store configuration information of the projected image; a user detection unit configured to detect a part of a user by using the captured image; an image-capturing area coordinates calculation unit configured to calculate image-capturing area coordinates for specifying a position of the image-capturing area in the projected image based on the captured image and the configuration information of the projected image when the part of the user is detected by the user detection unit; a position determination unit configured to determine, based on the image-capturing area coordinates, a position of an operation target image representing an image to be operated by the user such that a center of gravity of the operation target image is superimposed onto a center of gravity of the image-capturing area; a projected image generating unit configured to generate the projected image in which the operation target image is laid out on the determined position; and a projection control unit configured to control the projection unit to project the projected image.