# Lateral surface

Straight circular cylinder with unrolled lateral surface

The lateral surface of an object is the area of all the sides of the object, excluding the 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 ${\displaystyle a}$. 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 by the height of the prism.[1]

For a right circular cylinder of radius r and height h, the 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 ${\displaystyle r}$ is the radius of the circle at the bottom of the cone and ${\displaystyle l}$ 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 ${\displaystyle l={\sqrt {r^{2}+h^{2}}}}$ where ${\displaystyle h}$ is the height of the cone)

## References

1. ^ Geometry. Prentice Hall. p. 700.