The area of the nail where the nail plate cells are formed is the:

The matrix is the correct answer because it is the part of the nail bed located beneath the base of the nail where new nail cells are produced. This growth area is crucial for nail formation, as the cells produced in the matrix harden and eventually form the nail plate that we see.

The matrix is rich in keratin-producing cells, and as these cells mature and harden, they push older cells forward, resulting in the visible part of the nail. This process is essential for maintaining healthy nail growth.

The other terms refer to different parts of the nail structure. The free edge is the part of the nail that extends beyond the fingertip and is not involved in the actual creation of new cells. The extension is not a recognized term associated with nail anatomy. The lunula, which is the visible part of the matrix that appears as a whitish crescent at the base of the nail, does not represent the area where the nail cells are formed; rather, it is merely a part of the matrix that is visible externally.