Final answer:
The small cone-shaped area at the base of the hair follicle that fits into the hair bulb is the hair papilla, which contains connective tissue, blood capillaries, and nerve endings.
Step-by-step explanation:
The small cone-shaped area located at the base of the hair follicle that fits into the hair bulb is known as the hair papilla. The hair papilla is a mass of connective tissue, which houses blood capillaries and nerve endings essential for the nourishment and growth of the hair. It differs from the hair shaft, which is the visible part of the hair above the skin's surface, and the hair root, which is the part of the hair within the follicle and is the only living part. It is also distinct from the sebaceous gland, which produces sebum to lubricate the hair.