# Substituting into formulae

**Formulae**

A special type of equation which links two or more physical variables is called a **formula**.

An example of a formula is as follows:

*P* = 2(*l *+* w*)

Here, *P* represents the perimeter of a rectangle and *l* and *w* represent its length and width. This formula can be used to calculate the perimeter of any rectangle by **substituting** the values which are given in the formula.

Point to note:

When using formulas with real-life quantities such as mass, temperature, length etc, the variable will have units attached. These units are not included in the formula but should be provided with the answer.

**Substituting into formulae**

An example of substituting into formulae is as follows:

The formula of the surface area *S* of a cuboid is as follows:

S = 2*lw* + 2*lh* + 2*hw*

(*l* is the length, *w* is the width and *h* is the height).

What is the surface area given the following dimensions?

*l* = 150 cm

*w* = 32 cm

*h* = 25 cm (make sure all of the amounts are in the same units)

Substitute the values without the units

S = (2 x 150 x 32) + (2 x 150 x 25) + (2 x 25 x 32)

S = 9600 + 7500 + 1600

= 18,700 cm² (include the units in the answer)

This can also be written as 1.87m²