# Area and perimeter: Triangles and quadrilaterals

## In a nutshell

The perimeter and area are unique properties of every shape. The perimeter and area of triangles and quadrilaterals can be calculated using different formulae.

## Perimeter

The perimeter is the distance around the outside of a $2d$ shape. This is the sum of all the lengths of the outer sides of a given shape.

##### Example 1

*What is the perimeter of the shape below?*

* *

*Calculate the sum of all the outer sides.*

$4+3+5+2 = 14m$

*Therefore, the perimeter is *$\underline{14m}$*.*

**Note:** Ensure all the units are the same for each length before adding them together.

## Area

The area is the size of a shape's surface. There are different formulae to calculate the areas of different shapes. You will need to learn the following formulae.

**SHAPE** | **FORMULA** | **ILLUSTRATION** |

Triangle | $\text{Area}=\frac{1}{2}\times\text{base}\times\text{perpendicular\,height}$ $A=\dfrac{1}{2}bh$ | $b$ |

Rectangle | $\text{Area}=\text{length}\times\text{width}$ $A=lw$ | |

Parallelogram | $\text{Area}=\text{base}\times\text{perpendicular\,height}$ $A=bh$ | |

Trapezium | $\text{Area}=\dfrac{1}{2}\times(a+b)\times\text{height}$,
*$A=\dfrac{1}{2}(a+b)\times h$* | |

##### Example 2

*What is the area of the triangle below?*

*Identify the formula for the area of a triangle.*

${Area}=\dfrac{1}{2}\times{base}\times{perpendicular\,height}$

*Identify the relevant values. *

$\begin{aligned} &{Base} &= 4cm \\&{Perpendicular \ height} &= 4cm \end{aligned}$

**

*Place the values into the formula.*

${Area}=\dfrac{1}{2}\times 4 \times 4$

$\underline{{Area}=8 cm^2}$

*Note:** Area is measured in square units.*