This chapter establishes the mathematical framework for calculating the surface area of curved shapes in three-dimensional space. The primary methodology involves projecting a complex curved surface onto a flat two-dimensional coordinate plane, such as the horizontal plane or the vertical side planes. To account for the tilt and curvature of the surface, a scaling factor derived from the gradient vector is applied during the integration process. The text provides a generalized formula that utilizes the magnitude of the gradient and unit normal vectors to ensure accurate area calculation regardless of the chosen projection plane. Furthermore, the chapter demonstrates practical computation using MATLAB, showing how to define function handles and use specialized numerical integration commands to solve surface area problems that would be difficult to calculate manually.