Cuboid and its total surface area

## 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.

## 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.