A trapezium is a quadrilateral (4 sided shape) which has one pair of parallel sides. To find the area of a trapezium follow these simple steps:

1) Add up the parallel sides of the trapezium (a and b).

2) Multiply the answer from step 1 by the perpendicular distance between the two parallel sides (h).

3) Half the answer from step 2. Alternatively you might prefer to use the formula:

A = 1/2(a+b)h

Let's take a look at some examples of working out the area of a trapezium:

Example 1

Calculate the area of this trapezium: First of all let's work out the area of the trapezium using the three steps above:

1) Add up the parallel sides of the trapezium

6 + 10 = 16

2) Multiply the answer from step 1 by the perpendicular distance between the two parallel sides.

16 Ã— 3 = 48

3) Half the answer from step 2.

48 Ã· 2 = 24 cmÂ²

Now we are going to find the area of the trapezium using the formula.

a and b are 6 cm and 10 cm as these are the parallel sides.

h is 3 cm as this is the perpendicular distance between the two parallel sides.

So all you need to do is put these values into your formula for the area of a trapezium:

A = 1/2 (a+b)h

A =1/2 (6 + 10)3

A = 1/2 Ã— 16 Ã— 3

A = 24 cmÂ²

Let's take a look at another example on finding the area of a traqpezium.

Example 2

Calculate the area of this trapezium shown below. First of all let's use the three steps above to find the area of the trapezium.

1) Add up the parallel sides of the trapezium

17 + 23 = 40

2) Multiply the answer from step 1 by the perpendicular distance between the two parallel sides.

40 Ã— 15 = 600

3) Half the answer from step 2.

600 Ã· 2 = 300 cmÂ²

Now I will repeat this example but this time I will use the formula for the area of the trapezium.

a = 17cm b = 40cm and h = 15cm

Now all you need to do now is substitute these into your formula:

A = 1/2 (a+b)h

A =1/2(17 + 23)3

A = 1/2 Ã— 40 Ã— 15

A = 300 cmÂ²

Example 3

Work out the area of this picture frame which is shaped as a trapezium. On this example I will just use the formula method.

a and b are 10.6 cm and 14.8 cm as these are the parallel sides (the top and bottom of the picture frame)

h is 7 cm as this is the perpendicular distance between the two parallel sides.

So all you need to do is put these values into your formula for the area of a trapezium:

A = 1/2 (a+b)h

A =1/2 (10.6 + 14.8)7

A = 1/2 Ã— 25.4 Ã— 7

A = 88.9 cmÂ²