# Area

*Area* (A) is defined as the number of square units enclosed within a boundary, and is measured in the chosen unit of length squared (unit^{2}).

## Units of Area

It is common practice to use square metres (m^{2}) in engineering applications, particularly if the result is to be used in further calculations. For example, in mechanical engineering *pressure* is measured in *pascals* or N/m^{2}, while electrical engineers measure magnetic flux density in *teslas* or Wb/m^{2}.

Whatever units are used, it is important to be consistent in all calculations. All lengths should be confirmed to be in the chosen unit prior to use, or converted if necessary. For example, if all lengths are in centimetres then the resulting area will be in cm^{2}. The following table shows common units of length and their conversion factors.

Millimetres (mm) | Centimetres (cm) | Metres (m) |
---|---|---|

1 | 0.1 | 0.001 |

10 | 1 | 0.01 |

1,000 | 100 | 1 |

#### Worked Example 1

Find the area of a rectangle with horizontal and vertical sides 1.2 m and 70 cm respectively. Give your answer in m^{2}.

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The answer is required to be in m^{2}, so begin by converting all lengths to metres. Hence, *base* (b) = 1.2 m, *height* (h) = 0.7 m.

The area of a rectangle is given by A = b × h

= 1.2 × 0.7

= 0.84 m^{2}

See Areas of Basic Shapes for the area of a rectangle and other common shapes.

It is also possible to convert a previously calculated area into a different unit, in which case the area conversion rate will be the square of the length factor. For example, 1 m^{2} = 1,000,000 mm^{2}, since 1 m = 1,000 mm. Commonly used units of area and their alternatives are given in the table below.

Square millimetres (mm^{2}) | Square centimetres (cm^{2}) | Square metres (m^{2}) |
---|---|---|

1 | 0.01 | 0.000 001 |

100 | 1 | 0.000 1 |

1,000,000 | 10,000 | 1 |

#### Worked Example 2

Find the area from Worked Example 1 in cm^{2}.

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Although it is possible to recalculate the area from scratch, using b = 120 cm and h = 70 cm, the simplest approach is to convert the previous result of 0.84 m^{2} to cm^{2}.

1 m^{2} = 10,000 cm^{2}, hence,

A = 8,400 cm^{2}

## Mathematical Applicatons of Area

- Areas of Basic Shapes
- Compound Areas

Finding *area* may also be an intermediate step in the calculation of volume. For example, the volume of a *prism* is given by the area of the base multiplied by the height.

## Applications of Area in Engineering

Area is used in the calculation of a number of engineering quantities, including:

- electric flux density
- magnetic flux density
- pressure
- Resistivity