Lateral area is the area of the sides of a 3D geometric figure such as prism, cylinder or pyramid. Surface area is the total area of the given figure (the sides of a 3D geometric figure + base area).

For example, if we have a cube, then its lateral area formula is [tex]L=4a^2[/tex] and surface area formula is [tex]S=6a^2[/tex], because we added two bases with area [tex]a^2[/tex].

Another example is with a cone. Lateral area is [tex]L=\pi r l[/tex] and total surface area is [tex]S=\pi rl + \pi r^2[/tex], because we added the base area of a cone [tex]\pi r^2[/tex].