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# Lateral Area Formula

• Last Updated : 08 Dec, 2022

The concept of Lateral Area comes under the topic Mensuration which is a branch in mathematics that deals with measurements such as length, perimeter, area, volume, etc. for the 2-Dimensional/3-Dimensional geometrical figures. Mensuration studies geometric figure calculation and its parameters such as length, area, lateral surface area/curved surface area, volume, etc.

• The 2D Shapes are laid down on a plane by three or more straight lines or a closed segment. So they won’t have width or height. These 2D shapes have only length and breadth therefore area, and perimeter can be calculated.
• The 3D shape is a structure surrounded by a variety of surfaces/planes. These shapes are formed from various 2D shapes and they have length, breadth, and height. So we can find LSA, CSA, TSA, and Volume for 3D figures.

### Lateral Area Formula

The 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.

### Sample Problems

Question 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

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

Question 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

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

Question 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

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

Question 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

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

Question 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

The lateral surface area of hemisphere with given radius is 39.28 cm2.

Question 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

The lateral surface area of prism with given dimensions is 30 cm2.

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