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How to calculate the area of the trapezium (math help)

By Edited Dec 28, 2013 0 0

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.

trapezium 1

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:

trapezium 2

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 × 3 = 48

3) Half the answer from step 2.

48 ÷ 2 = 24 cm²

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 × 16 × 3

A = 24 cm²

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.

trapezium 3

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 × 15 = 600

3) Half the answer from step 2.

600 ÷ 2 = 300 cm²

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 × 40 × 15

A = 300 cm²

Example 3

Work out the area of this picture frame which is shaped as a trapezium.

trapezium 4

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 × 25.4 × 7

A = 88.9 cm²

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