# Substitute into common formulae

Lesson

Mathematicians love to write formulae as algebraic shorthand for expressions that we would otherwise have to write as a sentence.

For example, instead of writing, "The area of a rectangle is calculated by multiplying the length by the width," I can write the algebraic formula $A=lb$A=lb. Much shorter right! Formulae also makes it easier to substitute values and evaluate equations.

There are lots of topics that have common formulae: simple interest, area, volume, perimeter and temperature conversions just to name a few. Make sure your familiar with the formulae for your topic before you start doing exercises.

Here are some examples to get you started.

#### Examples

##### question 1

The perimeter of a square with side lengths of $a$a is given by the formula $P=4\times a$P=4×a.

Find $P$P if the length of each side is $5$5 cm.

##### question 2

The area of a triangle is given by the formula $A=\frac{1}{2}$A=12$($(base$\times$×height$)$).

If the base of a triangle is $3$3 cm and its height is $10$10 cm, find its area.

##### Question 3

The simple interest generated by an investment is given by the formula $I=\frac{P\times R\times T}{100}$I=P×R×T100.

Given that $P=1000$P=1000, $R=6$R=6 and $T=7$T=7, find the interest generated.