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.

        

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.

       

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.