# Area of a trapezium

## What is a Trapezium?

A trapezium is a quadrilateral: a polygon with four sides. It has exactly one pair of parallel sides.

The area of a trapezium is the amount of space inside the trapezium. It is measured in units squared ( etc).

## Different types of trapezia

Trapezia can be categorised by their properties, such as the length of their sides or the size of their angles.

An isosceles trapezium is a trapezium where the base angles are equal and therefore the left and right side diagonal lengths are also equal.

A scalene trapezium is a trapezium where the base angles and the diagonal lengths are not equal.

An isoceles trapezium

A scalene trapezium

## How to find the area of a trapezium

For most regular quadrilaterals, such as a square or a rectangle, you can find the area of the shape simply by multiplying the height of the quadrilateral by the width (area of a quadrilateral = height x width).

Trapezia are a special case as their width is not always constant.

To find the area of a trapezium, follow these simple steps:

1. Find the sum of the parallel sides
2. Divide the sum by
3. Multiplying the average width by the perpendicular height.

Why not download our FREE Area and Perimeter of 2D shapes poster?

Formula for the area of a trapezium

The area of a trapezium can also be summarised with the following formula:

$A&space;=&space;\left&space;(\frac{a+b}{2}&space;&space;\right&space;)&space;h$

Calculating the area of a trapezium

You can use the formula to calculate the area of trapezium three and trapezium four below:

Trapezium three

a = 4 cm

b = 6 cm

h = 6 cm

$A&space;=&space;&space;\left&space;(&space;\frac{a+b}{2}&space;\right&space;)&space;h$
$A&space;=&space;&space;\left&space;(&space;\frac{4+6}{2}&space;\right&space;)&space;6$
$A&space;=&space;&space;\left&space;(&space;\frac{10}{2}&space;\right&space;)&space;6$
$A&space;=&space;&space;5\times&space;&space;6$

A = 30 cm2

Trapezium four

a = 4 cm

b = 5 cm

h = 6 cm

$A&space;=&space;\left&space;(\frac{a+b}{2}&space;&space;\right&space;)&space;h$
$A&space;=&space;\left&space;(\frac{4+5}{2}&space;&space;\right&space;)&space;6$
$A&space;=&space;\left&space;(\frac{9}{2}&space;&space;\right&space;)&space;6$

A = 4.5 x 6

A = 27 cm2

## Misconceptions

Here are the most common misconceptions to look out for:

1. Children confuse the length of the diagonal with the height a trapezium.

2. Children do not understanding that area is a two dimensional measure.

3. Children forget to include the unit of measurement in their answer (e.g. cm2); and

4. Children do not observe when a problem offers different units of measure for the given lengths - e.g. cm and m.

## Fun ways to teach children how to find the area of a trapezium

Provide children with rectangular sheets of sugar paper (a variety of different sizes is best). Ask every child to create their own unique trapezium using a ruler. It can be whatever size and shape they want (though you may want to challenge some children to create isoceles trapezia) and they can use two lengths of the paper as the pair of parallel sides. Now, you have 30 different trapezia you can stick around the classroom, ready for the children to measure and calculate the area for.

You might enjoy sharing this catchy how to find the area of a trapezium song with your class.

Looking for fantastic resources to engage your children in their maths learning? Check out our Year 6 Calculating Compound Shapes unit.