Lateral Area Formula
The lateral area formula is used to find the lateral area of any solid object. The lateral area of any figure is the area of the nonbase faces only. Lateral area formulas help in calculating the lateral surface area of different figures including cuboid, cube, cylinder, cone, and sphere. Every 3dimensional object has a lateral area that can be touched. Let us see more about the lateral area formula along with a few solved examples.
What is the Lateral Area Formula?
The lateral area formula for different types of objects is different. Hence there are many lateral area formulas which are explained below. The lateral area does not include the base area of the object as well as the face parallel to the base. The lateral area formula for various objects are:
 Lateral area of Cuboid
The lateral surface area formula of a cuboid is given by:
Lateral area of cuboid = 2(length + breadth) × height
 Lateral area of Cube
The lateral surface area formula of a cube of the side “a” is given by:
Lateral area of cube = 4 × (side)^{2}
 Lateral Area for Cylinder
The Curved or lateral Surface Area formula of a Cylinder is given by:
Lateral area of cylinder = 2 × π × r × h
where,
 r = base radius, and
 h = height of the cylinder.
 Lateral Area for Cone
The Curved Surface Area formula of a Cone (lateral) is given by:
Lateral area of cone = π × r × l
where, r = base radius, and l = slant height.
Slant height:
(l) = \( \sqrt{ r^2 + h^2 }\)
where,
 h = height of cone.
 Lateral Area for Sphere
The lateral surface area formula of a sphere is given by:
Lateral area of sphere = 4πr^{2}
where
 r is the radius of the sphere.
 Lateral Area for Hemisphere
The curved or lateral Surface Area (CSA) formula of a Hemisphere is given by:
Lateral area of Hemisphere = 2πr^{2}
where
 r is the radius of the sphere of which the hemisphere is a part.
Solved Examples Using Lateral Area Formula

Example 1: The length breadth of a cuboid is 6 units, 2 units, and 16 units respectively. Calculate the lateral surface area of the cuboid. Also, find the length of side of equal lateral surface area to this cuboid. Use lateral area formula to solve this.
Solution:
To find: Lateral formula of cuboid, length of the side of a cube
Given:
Length of cuboid = 6 units
Breadth of cuboid = 2 units
Height of cuboid = 16 units
Lateral area of cube = Lateral area of a cuboid
Using lateral area formula of cuboid,
Lateral area of cuboid = 2(length + breadth) × height
= 2( 6 + 2 ) × 16
= 256 units
Also, Lateral surface area of cube = Lateral surface area of a cuboid
The lateral surface area of cube = 256 units
Using the lateral surface area formula of the cube,
4 × (side)^{2 }= 256 units
side = \(\sqrt{256}\) = 8 units
Answer: Lateral area of cuboid = 256 units, and Length of the side of cube = 8 units

Example 2: The radius of a sphere measures 4 units. This sphere is cut into two equal halves. Calculate the lateral surface areas of both objects by using the lateral area formula.
Solution:
To find: Lateral surface area of sphere and hemisphere
Given:
Radius of sphere and hemisphere = 4 units
Using lateral area formula,
Lateral area of sphere = 4πr^{2}
= 4 × π × (4)^{2}
= 201.142 units
Lateral/ curved surface area of hemisphere = 4πr^{2}
= 2 × π × (4)^{2}
= 100.571 units
Answer: Lateral area of sphere = 201.142 units, and Lateral/ curved surface area of hemisphere = 100.571 units