**Objective**

To form a cuboid and find the formula for its total surface area

**What is a Cuboid?**

- A cuboid is a three-dimensional solid shape that has 6 faces, 8 vertices, and 12 edges.
- It is one of the most commonly seen shapes around us and has three dimensions: length, width, and height.

**Fig.(1) Cuboid**

**Total Surface Area of Cuboid**

- The surface area of any three-dimensional shape is the total region covered by all its faces.
- In the same way, the total surface area of a cuboid is the sum of the areas of all its six rectangular faces.
- The formulas for these can be derived from the figure given below.

**Fig.(2) Cuboid with dimensions**

**Total surface area**

- Area of face EFGH = Area of Face ABCD = (a × b)
- Area of face BFGC = Area of face AEHD = (b × c)
- Area of face DHGC = Area of face ABFE = (a × c)
- Total surface area of a cuboid = Sum of the areas of all its 6 rectangular faces
- = Area of (ABCD + EFGH + BFGC + AEHD + DHGC + ABFE)= 2ab + 2bc + 2ac= 2(ab + bc + ac) square units.

**Pre-requisite Knowledge**

**Rectangle :**

A rectangle is a parallelogram in which one angle is 90°.

**Area of a Rectangle:**

- The amount of region enclosed by a plane closed figure is called its area.
- Area of a rectangle = length × breadth

**What is net of a cuboid?**

- When we unfold a cuboid by its faces 2D shape called the net of the cuboid.
- If we fold a net of cuboid, we will get cuboid.