Lateral surface

The lateral surface of an object is the area of all the sides of object excluding area of its base and top.

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 A_face = 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 by 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.

For a cone, the Lateral Surface Area would be ${\displaystyle \pi rl}$ where $r$ is the radius of the circle at the bottom of the cone and $l$ is the lateral height (the length of a line segment from the apex of the cone along its side to its base) of the cone (given by the Pythagorean theorem $l=\sqrt{r^2+h^2}$ where $h$ is the height of the cone)

References

1. Geometry. Prentice Hall. p. 700.

Further reading

• Lateral surface at Mathwords