The lateral surface of an object is all of the sides of the object, excluding its bases (when they exist).

Lateral Surface Area

The ''lateral surface area'' is the area of the lateral surface. This is to be distinguished from the ''total surface area'', which is the lateral surface area together with the areas of the base and top. For a

cube A cube or regular hexahedron is a three-dimensional space, three-dimensional solid object in geometry, which is bounded by six congruent square (geometry), square faces, a type of polyhedron. It has twelve congruent edges and eight vertices. It i ...

the lateral surface area would be the area of the four sides. If the edge of the cube has length , the area of one square face . Thus the lateral surface of a cube will be the area of four faces: . More generally, the lateral surface area of a

prism PRISM is a code name for a program under which the United States National Security Agency (NSA) collects internet communications from various U.S. internet companies. The program is also known by the SIGAD . PRISM collects stored internet ...

is the sum of the areas of the sides of the prism. This lateral surface area can be calculated by multiplying the

perimeter A perimeter is the length of a closed boundary that encompasses, surrounds, or outlines either a two-dimensional shape or a one-dimensional line. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimet ...

of the base by the height of the prism. For a

right circular cylinder A right circular cylinder is a cylinder whose generatrices are perpendicular to the bases. Thus, in a right circular cylinder, the generatrix and the height have the same measurements. It is also less often called a cylinder of revolution, beca ...

of radius and height , the lateral area is the area of the side surface of the cylinder: . For a

pyramid A pyramid () is a structure whose visible surfaces are triangular in broad outline and converge toward the top, making the appearance roughly a pyramid in the geometric sense. The base of a pyramid can be of any polygon shape, such as trian ...

, 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 In geometry, a cone is a three-dimensional figure that tapers smoothly from a flat base (typically a circle) to a point not contained in the base, called the '' apex'' or '' vertex''. A cone is formed by a set of line segments, half-lines ...

, the lateral surface area would be where is the radius of the circle at the bottom of the cone and 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 In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite t ...

where is the height of the cone)

Lateral Surface Area

References

Further reading