# Surface Area Of Cuboid

A cuboid is a three-dimensional figure bounded made up of six rectangular planes, having a 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.

A cuboid(3-dimensional) can be seen made up of three rectangles(2-dimensional) of different dimension when seen from any of the ends. The other three rectangular surface is replicate of the rectangle present opposite to them.

Thus a cuboid has six rectangular sides, called faces, and each face of a cuboid is a rectangle, and all of 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 surface area of the Cuboid can be of two types-

(i) Total Surface Area

(ii) Lateral Surface Area (Curved Surface Area)

## 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.

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 length=8 cm, width=6 cm and height=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 cm2.

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 Surface area 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$77.2 (4.8 + 3.4)

= 14.4 (8.2)

= 118.80 cm²