hexa calculatorhexacalculator.com logo

Cuboid Surface Area Calculator

Introduction

Welcome to our Cuboid Surface Area Calculator, which will help you calculate the Lateral and Total Surface Area of the Cuboid. A cuboid is a solid three-dimensional shape with six faces, twelve edges, and eight vertices. This is very similar to the cube, but the difference between a cuboid and a cube is that the cuboid’s faces are not necessarily squares. The cuboid has three dimensions length, width, and height.

The total surface area of a cuboid is the total area of all 6 of its faces. The cuboid’s lateral surface area is the cuboid’s surface area without the top and bottom faces.

How to use Cuboid Surface Area Calculator?

Using the Cuboid Surface Area Calculator, you can calculate the lateral surface area and the cuboid’s total surface area by inputting the cuboid’s dimensions, like length, height, and breadth, for the calculation.

The variables in the Cuboid Surface Area Calculator include

Length (l)
The Length of the Cuboid.

Breadth (b) The Breadth of the Cuboid.

Height (h)
The Height of the Cuboid.

Lateral Surface Area (LSA)
We can calculate the Lateral Surface Area of the cuboid by using the following formula

LSA=2h(l+b)\text{LSA} = 2h(l + b)

Total Surface Area (TSA)
We can calculate the Total Surface Area of the cuboid by using the following formula

TSA=2(lb+bh+hl)\text{TSA} = 2(lb + bh + hl)

What is a Cuboid?

A cuboid is a solid three-dimensional shape with six faces, twelve edges, and eight vertices. The cuboid’s faces are rectangular. The angles formed at the vertices of the cuboid are all 90 degrees.

The cuboid has three dimensions length, breadth (width), and height. The length of the vertical edge is considered as the height, and on one of the rectangular faces of the cuboid, the length of the longer edge is considered the length, and the length of the shorter edge is considered the breadth.

Properties of a Cuboid

  1. The cuboid has six faces, twelve edges, and eight vertices.
  2. The faces of the cuboid are rectangular in shape.
  3. The opposite edges of the cuboid are parallel to each other.
  4. The dimensions of the cuboid include length, breadth, and height.
  5. Angles formed at the vertices of the cuboid all measure 90 degrees.

How is the Lateral Surface Area of Cuboid Calculated?

The lateral surface area of the cuboid is the sum of areas of the faces of the cuboid except for the top and bottom faces.

The lateral surface area of the cuboid can be calculated using the following formula.

LSA=2h(l+b)\text{LSA} = 2h(l + b)

Where

l = Length of the Cuboid

b = Breadth of the Cuboid

h = Height of the Cuboid

How is the Total Surface Area of Cuboid Calculated?

The Total surface area of the cuboid is the sum of the areas of all six faces of the cuboid.

We can calculate the total surface area of the cuboid by using the following formula

TSA=2(lb+bh+hl)\text{TSA} = 2(lb + bh + hl)

Where,

l = Length of the Cuboid

b = Breadth of the Cuboid

h = Height of the Cuboid

Example

Given a cuboid of length 6 cm, breadth 4 cm, and height 3 cm. What are the lateral surface area and total surface area of the cuboid?

We can calculate the lateral and total surface area using the following formulas.

Lateral Surface Area of Cuboid

LSA=2h(l+b)=2×3×(6+4)=6×10=60  cm2\begin{aligned} \text{LSA} &= 2h(l + b) \\[10pt] &= 2 \times 3\times (6 + 4) \\[10pt] &= 6 \times 10 \\[10pt] &= 60 \; cm^2 \end{aligned}

Total Surface Area of Cuboid

TSA=2(lb+bh+hl)=2×(6⋅4+4⋅3+3⋅6)=2×54=108  cm2\begin{aligned} \text{TSA} &= 2(lb + bh + hl) \\[10pt] &= 2 \times (6\cdot4 + 4\cdot3+3\cdot6) \\[10pt] &= 2 \times 54 \\[10pt] &= 108 \; cm^2 \end{aligned}

As you can see from the above calculation, the lateral surface area of the cuboid is 60 sq cm, and the total surface area of the cuboid is 108 sq cm.

Author

hexacalculator design team

Our team blends expertise in mathematics, finance, engineering, physics, and statistics to create advanced, user-friendly calculators. We ensure accuracy, robustness, and simplicity, catering to professionals, students, and enthusiasts. Our diverse skills make complex calculations accessible and reliable for all users.

You might also like