**What is Cuboid?**

A cuboid is a three dimensional figure bounded by six rectangular planes,having different magnitude of length, width and height. If you look around and you can see a box, a brick or anything in the shape of a rectangular could be cuboid.

It has six rectangular sides, called faces, and each face of a cuboid is a rectangle, and all of a its corners are 90-degree angle

**Surface Area of Cuboid**

A common mistake is to confuse area with the volume of cuboids, which are totally different aspect. The total surface area (TSA) of a cuboid is the sum of the areas of its 6 faces.

**Formula for Surface Area of Cuboid:**

Before going into the concept of area, let us denote the dimensions of a cuboid, which are,

Length, Width and Height which are represented by l, w, h respectively.

The Total surface area of a cuboid (TSA) is equal to the sum of the areas of it’s 6 rectangular faces, which is given by:

*TSA = 2 (lw + wh + lh) *

The above formula gives the total surface area of a cuboid having all the six sides. However, there is one more term which is commonly used for measurement of area of a cuboid, which is the lateral surface area of a cuboid (LSA).

The lateral surface area of a cuboid is the sum of 4 planes of a rectangle, leaving the top (upper) and the base (lower) a. Mathematically, LSA is given as:

*LSA = 2 (lh + wh) = 2 h (l + w)*

**Example of Surface Area of Cuboid**

**Example 1**:** Given below is a cuboid having it’s dimension given as l=8 cm, w=6 cm and h=5 cm, find the TSA of a cuboid.**

**Solution**

Given:

*h = 5 cm*

*w = 6 cm*

*l = 8 cm*

Using the formula: *TSA = 2 (lw + wh + hl) *

=\(2(8 \times 6 + 6 \times 5 + 5 \times 8)\)

= \(2(48 + 30 + 40)\)

= 2(118)

= 236

So, the total surface area of this cuboid is 236 cm^{2}.

**Example 2:** **The dimensions of a cuboid are given as follows:**

**Length = 4.8 cm**

**Width = 3.4 cm **

**Height = 7.2 cm.**

**Find the Total and the Lateral Surface area.**

**Solution:**

The total surface area is given as

*TSA = 2 (lw + wh + hl)*

=\(2(4.8 \times 3.4 + 3.4 \times 7.2 + 7.2 \times 4.8)\)

= \(2(34.56+ 24.48 + 16.32)\)

= 2(75.36) cm²

**TSA** = 150.72 cm

Also, the lateral surface area = 2 h (l + w)

= 2 \(\times\)7.2 (4.8 + 3.4)

= 14.4 (8.2)

= 53.76 cm²