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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.

Geometry. Prentice Hall. p. 700.

Further reading

Lateral surface at Mathwords

Undergraduate Texts in Mathematics

Graduate Texts in Mathematics

Graduate Studies in Mathematics

Mathematics Encyclopedia

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