Example 8 Work out the area of this parallelogram. The formula for the area of a parallelogram is:
6 cm
A = bh A = 6 × 10 = 60 cm2
10 cm
Area of a trapezium
a
To work out the area of a trapezium, you need to know the length of its two parallel sides, a and b, and the perpendicular height, h, between the parallel sides.
h
The diagram below shows how you can fit the trapezium together with another one that is exactly the same, to form a parallelogram. The area of each trapezium is half the area of the parallelogram.
b
You know that the area of a parallelogram is base times height.
So, the area of a trapezium is: 1 2
× sum of the lengths of the parallel sides × height
You can write this as a formula, where A represents the area, a and b are the lengths of the parallel sides and h is the height: A=
1 2
× (a + b) × h or A = 12 (a + b)h
Hint
You must add the numbers in the brackets before doing anything else.
Example 9 Work out the area of this trapezium.
5 cm
The formula for the area of a trapezium is: A = 12 (a + b)h A=
× (9 + 5) × 4 14 × 4 = 2 = 28 cm2
60
4 cm
1 2
9 cm
3 Perimeter, area and volume
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