A three-dimensional solid's lateral area is the surface area of its sides, excluding its top and bottom. A cube has six face -- its lateral surface area is the area of four of those sides, since it doesn't include the top and bottom.
You can find the lateral area of a solid with parallel bases by multiplying the perimeter of the base (the length around the edge of the base) by the solid's height.
The perimeter of a cube's base is equal to four times the length of one of the cube's edges, s. The height of the cube is also equal to s. So lateral area, LA, is equal to 4s multiplied by s.
Hence, the formula - LA = 4s².
Example:
The side of a cube is 4cm. Find its lateral surface area.
Solution:
Where e is side.
Given that e = 4cm.
Lateral surface area = 4 * e².
=4 * 4²
=4 * 16
= 64 sq. cm.
To learn more, see Andrews.edu's Lateral & Surface Areas, Volumes.