# Total surface area of cuboid formula explained

Learn and know what is the formula for finding the total surface area of cuboid in mensuration chapter. For a cuboid there are 4 important formulas are there. The 4 formulas that we have to learn in case of cuboid are first is volume of a cuboid, second is lateral surface area of a cuboid, third is diagonal of a cuboid and fourth is total surface area of a cuboid. Lateral surface area in short form we say as L.S.A and total surface area in short form we say as T.S.A. now we will know what is total surface area of cuboid and the formula to find it. I have given derivation of T.S.A i.e. how we got T.S.A of cuboid formula, so just check that also.

## What is a cuboid?

Generally in this universe we will observe so many shapes. In that some will be of cuboid shape also. Then what is a cuboid? Cubiod is a 3D figure. Cuboid is 3 dimensional figure of rectangle. Cuboid has 3 dimensions i.e. length, breadth and height.

### What is total surface area meaning?

For any 3D figure, the area of total faces of the figure we call as total surface area. For example, in cuboid there are totally six rectangular faces. The sum of areas of all the six faces is called as T.S.A i.e total surface area of cuboid.

#### Derivation for total surface area of cuboid formula

We know that, the 6 faces of cuboid are in the shape of rectangle. To get the formula for the total surface area of a cuboid (T.S.A) we need to find sum of all these areas. Observe the diagram, all the 6 faces i have marked with different colours. So, now one by one area am going to add for deriving the formula for total surface area.

The Total surface area (T.S.A) of cuboid

= L × H + B × H + L × H + B × H + L × B + L × B

= 2 × L × B + 2 × B × H + 2 × H × L

= 2 × (LB + BH+ HL) (I took 2 as common in all the terms)

Therefore, the formula for finding the value of T.S.A of cuboid = 2 (LB + BH+ HL)

##### How to find T.S.A by using the formula?

To calculate T.S.A of cuboid we should know the values of length, breadth and height. For example, if length is 10 cm, breadth is 7 cm and height is 12 cm then T.S.A = 2 (10 × 7 + 7 × 12+ 12 × 10)  = 2 (70 + 84 + 120) = 2 (274) = 548 square centimetre. 