What is the formula for the area of a trapezium?

The formula for the area of a trapezium is: \(\frac{1}{2} \times (a + b) \times h\).

A trapezium is a four-sided shape with at least one pair of parallel sides. These parallel sides are referred to as the bases of the trapezium, and they are usually labelled as \(a\) and \(b\). The height (\(h\)) is the perpendicular distance between these two bases.

To find the area of a trapezium, you need to add the lengths of the two parallel sides (\(a\) and \(b\)), then multiply this sum by the height (\(h\)). Finally, you divide the result by 2. This formula can be written as:

\[ \text{Area} = \frac{1}{2} \times (a + b) \times h \]

For example, if you have a trapezium where the lengths of the parallel sides are 8 cm and 5 cm, and the height is 4 cm, you would substitute these values into the formula like this:

\[ \text{Area} = \frac{1}{2} \times (8 + 5) \times 4 \]

First, add the lengths of the parallel sides:

\[ 8 + 5 = 13 \]

Next, multiply this sum by the height:

\[ 13 \times 4 = 52 \]

Finally, divide by 2 to find the area:

\[ \frac{52}{2} = 26 \]

So, the area of the trapezium is 26 square centimetres. This formula is very useful for solving problems involving trapeziums in your GCSE Maths exams.