Areas of three-dimensional figures

Area of three-dimensional figures

Three-dimensional figures are solid figures which have three dimensions namely; length, width and height. Examples of these figures are rectangular prisms, cubes and cylinders. In this section, you will learn to find areas and volumes of three dimensional figures.

Surface areas of three-dimensional figures

Three-dimensional figures are formed by plane surfaces. Rectangular prisms, cubes and cylinders are examples of three-dimensional figures.

You have learnt plane figures and how to find their areas. In this section, you will learn to find the surface areas of three-dimensional figures.

Example 1

Find the surface area of the following rectangular prism:

Solution

There are 6 faces in the rectangular prism. Thus, the surface area of the rectangular prism is given by:

Surface area = length × width × 2 + length × height × 2 + width × height × 2

= (30 cm × 15 cm) × 2 + (30 cm × 20 cm) × 2 + (15 cm × 20 cm) × 2

= 450 cm² × 2 + 600 cm² × 2 + 300 cm² × 2

= 900 cm² + 1,200 cm² + 600 cm²

= 2,700 cm²

Therefore, the surface area of the rectangular prism is 2,700 cm²

Example 2

Find the surface area of a cube of length 30 cm.

Solution

Since all the six sides of the cube are equal, the surface area of the cube is obtained by using the formula:

The surface area of a cube = length × length × 6

= 30 cm × 30 cm × 6

= 5,400 cm²

Therefore, the surface area of the cube is 5,400 cm²