Final answer:
The dermal papillae are the structure responsible for increasing the surface area and providing for the strength of attachment between the epidermis and dermis. They are associated with the stratum basale, which is the deepest epidermal layer.
Step-by-step explanation:
The structure responsible for increasing surface area to provide for the strength of attachment between the epidermis and dermis is known as dermal papillae. These finger-like projections, or folds, enhance the connection by increasing the surface area where the epidermis and dermis bond, primarily through intertwining collagen fibers which are part of the basement membrane.
The correct answer to the question is not explicitly listed, but it's important to recognize the relevance of the stratum basale. This layer of the epidermis houses the cells that bond to the dermis via the basement membrane and contribute to the interlocking of dermal papillae.
Dermal papillae are essential in providing the increased strength of attachment, hence, they are closely associated with the stratum basale of the epidermis due to their location and function.