Final answer:
The cell cortex, consisting of crosslinked actin filaments that form the cytoskeleton, determines a cell's shape and the mechanical properties of its plasma membrane.
Step-by-step explanation:
The shape of a cell and the mechanical properties of its plasma membrane are determined by a meshwork of fibrous proteins called the cell cortex. This meshwork is found underneath the plasma membrane and consists of crosslinked actin filaments. These filaments are part of the cytoskeleton, which maintains the shape of the cell, secures some organelles in specific positions, and allows cytoplasm and vesicles to move within the cell. Additionally, proteins and carbohydrates extend from the plasma membrane's outward-facing surface, contributing to the cell's interaction with its environment.