The lateral surface of an object is all of the sides of the object, excluding its base and top (when they exist). 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 In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. Viewed from a corner it is a hexagon and its net is usually depicted as a cross. The cube is the only ...

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 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 a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several pr ...

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

cylinder A cylinder (from ) has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base. A cylinder may also be defined as an ...

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

pyramid A pyramid (from el, πυραμίς ') is a structure whose outer surfaces are triangular and converge to a single step at the top, making the shape roughly a pyramid in the geometric sense. The base of a pyramid can be trilateral, quadrilate ...

, 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 A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex. A cone is formed by a set of line segments, half-lines, or lines con ...

, 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 opposit ...

where is the height of the cone)

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Further reading