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The lateral surface of a geometric solid is the face or surface of the sides of the solid. That is, the surface of all faces or sides that are not a base side.

For a cube, the lateral surface area would be the area of four sides. Consider the edge of the cube as a. The area of one square face Aface = a ⋅• a = a2. Thus the lateral surface of a cube will be the area of four faces: a ⋅ a ⋅ 4 = 4a2. The lateral surface can also be calculated by multiplying the perimeter of the base to the height of the prism.[1]

For a cylinder, lateral area is the area of the side surface of the cylinder: A = 2πrh.

For a pyramid, the lateral surface area is the sum of the areas of all of the triangular faces but excluding the area of the base.
References

Geometry. Prentice Hall. p. 700.