Area is the measure of a two-dimensional space enclosed by a shape, and surface area is the sum of all the areas of the faces of a three-dimensional solid.
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surface area is the area of a 3D object radius is half of the diameter of a circle
Lateral area excludes the areas of the top and bottom faces, which are included in the surface area.
The surface area of a box is the sum of the areas of the individual faces. If that's what you said, then there is no difference.
Curved surface area includes the area of the length of the cylinder only whereas surface area includes the two bases as well...