Chapter Overview Maths

Exam board

Pearson Edexcel

Number

Algebra

Graphs

Ratio proportion and rates of change

Shapes and area

Angles and geometry

Trigonometry

Probability

Statistics

Maths

# Area and perimeter: Formulae 0%

Summary

# Area and perimeter: Formulae

## ​​In a nutshell

The perimeter and area of triangles and quadrilaterals can be calculated with their own formula. These formulae can also be applied to finding the area and perimeter of compound shapes.

### Area and perimeter - definitions

The perimeter of a shape is the sum of the lengths of the outer sides of the shape.

The area of a shape tells you the size of the surface of the shape.

## Area formulae

These are the following formulae you need to know.

#### illustration

Triangle

$\text{Area}=\frac{1}{2}\times\text{base}\times\text{perpendicular\,height}$​​

$A=\frac{1}{2}bh$​​

$b$​​

Square

$\text{Area}=\text{length}^2$​​

$A=x^2$​​

​​

$x$​​

Rectangle

$\text{Area}=\text{length}\times\text{width}$​​

$A=lw$​​

Parallelogram

$\text{Area}=\text{base}\times\text{perpendicular\,height}$​​

$A=bh$​​

Trapezium

$\text{Area}=\frac{1}{2}\times(a+b)\times\text{height}$,

$A=\frac{1}{2}(a+b)\times h$​​

where $a$ and $b$ are the lengths of the two parallel sides.

## Area and perimeter problems

You can use the formulae for the areas and perimeters of triangles and quadrilaterals to solve problems involving more complex shapes.

##### Example 1

In the diagram below, let $a=5m,b=9m,c=4m$