Lateral Area Formula

Lateral area of a three-dimensional object is the surface area of all its sides, excluding the bases (top and bottom surfaces). In this article, we will learn about, lateral area formulas along with related examples and others in detail.

Lateral area formula finds the lateral area for a figure. The Lateral area is an area of non-base faces of a figure i.e., It doesn’t include the base area of the figure as well as the face parallel to the base. The Lateral area can also be called a lateral surface area. This formula is useful in calculating the Lateral area for different kinds of figures like cubes, cuboids, cones, cylinders, prisms, pyramids, spheres, hemispheres, etc.

The below table consists of Lateral Area formulas for different kinds of figures.

Example 1: Find the Lateral area for the cube with each side of the length of 4cm.

Solution:

Given,

Side length (a) = 4cm

Lateral Area of cube = 4a²

= 4(4)²

= 4 ×16

= 64cm²

Lateral surface area of a cube with given dimensions is 64cm².

Example 2: Find the lateral surface area of the sphere with a radius of 2 units.

Solution:

Given,

Radius of sphere (r) = 2 units

Lateral Area of sphere = 4πr²

= 4 × (22/7) × (2)²

= (4 × 22 × 4)/7

= 352/7

= 50.28 square units

Lateral surface area of sphere with given radius is 50.28 square units.

Example 3: Find the Lateral area for the cuboid with dimensions of length = 4cm, breadth = 2cm and height = 2cm.

Solution:

Given,

length (l) = 4cm, breadth (b) = 2cm, height (h) = 2cm

Lateral Area of cuboid = 2h(l + b)

= 2(2)(4 + 2)

= 4 × 6

= 24cm²

Lateral surface area of a cuboid with given dimensions is 24cm².

Example 4: Find the lateral surface area of the cone with a base radius of 3 units and a slant height of 5 units.

Solution:

Given,

Base radius of cone (r) = 3 units

Slant Height (l) = 5 units

Lateral Area of cone = πrl

= (22/7) × 3 × 5

= (22 × 3 × 5)/7

= 330/7

= 47.14 square units

Lateral surface area of sphere with given radius is 47.14 square units.

Example 5: Find the lateral surface area of the hemisphere with a radius of 2.5cm.

Solution:

Given,

Radius of hemisphere (r) = 2.5cm

Lateral Area of sphere = 2πr²

= 2 × (22/7) × (2.5)²

= (44/7) × 6.25

= (44 × 6.25)/7

= 275/7

= 39.28 cm²

Lateral surface area of hemisphere with given radius is 39.28 cm².

Example 6: Find the lateral surface area of the prism which is having a perimeter of base = 10cm and a height = 3cm.

Solution:

Given,

Perimeter of base = 10cm

Height = 3cm

Lateral Surface area = Perimeter of base × height

= 10 × 3

= 30 cm²

Lateral surface area of prism with given dimensions is 30 cm².

What Is the Lateral Area Formula of Cone?

Lateral area formula for cone is, LSA = πrl. Where r is the radius of a cone, l is the slant height of the cone, and π (pi) is a constant term with a value of 3.14 or 22/7.

What Is the Lateral Area Formula of Sphere?

Lateral area formula of sphere is, LSA = 4πr². Where r is the radius of a sphere, h is the height of the sphere, and π (pi) is a constant term with a value of 3.14 or 22/7.

What Is the Lateral Area Formula of Cylinder?

Lateral area formula of cylinder is, LSA = 2πrh. Where r is the radius of a circular base of the cylinder, h is the height of the cylinder, and π (pi) is a constant term with a value of 3.14 or 22/7.

What Is the Lateral Area Formula of Cuboid?

Lateral area formula of cuboid is, LSA = 2 (l+ b). Where h is the height of the cuboid, l is the length of the cuboid, and b is the breadth of the cuboid.

What Is the Lateral Area Formula of Cube?

Lateral area formula of cuboid is, LSA = 4(a)². Where a is the side of the cube.