Key points
While rectangles look alike and are easily recognisable, trapeziumA quadrilateral with exactly one pair of parallel sides. can look very different to each other.
Two identical trapeziums can be combined to make a parallelogramA quadrilateral with opposite pairs of sides that are both equal in length and parallel. Opposite angles are equal. or a rectangle. The areaA measure of the size of any plane surface or 2D shape. Area is measured in square units, for example, square centimetres or square metres: cm虏 or m虏. of the trapezium is half of the parallelogram or rectangle.
Recognising the parallelAlways equidistant (at equal distances). Parallel lines, curves and planes never meet however far they extend. sides and the perpendicularPerpendicular lines are at 90掳 (right angles) to each other. height are key in working out the area of a trapezium. The area of a trapezium is the average length of its parallel sides multiplied by the perpendicular height. This is shown by the formulaA fact, rule, or principle that is expressed in words or in mathematical symbols. Plural: formulae. 饾懆 = 陆 (饾拏 + 饾拑)饾拤.
The parallel sides of a trapezium are labelled 饾拏 and 饾拑. The perpendicular height is the shortest distance between the parallel sides and is labelled 饾拤.
Video
Watch the video to learn how to work out the area of a trapezium.
Understanding the formula for the area of a trapezium
To find the area of a trapezium:
- Draw two congruentA shape that has a mathematical change of appearance. trapeziums.
- Rotate one trapezium by 180掳.
- Put the two trapeziums together to form a parallelogram.
- The area of the parallelogram is the base multiplied by the perpendicular height. The base of the parallelogram is the total of the two parallel sides of the trapezium, (饾拏 + 饾拑). The area of the parallelogram is (饾拏 + 饾拑)饾拤.
- The area of the trapezium is half of the area of the parallelogram. The formula is陆(饾拏 + 饾拑)饾拤.
When the trapezium has two right angles, the two congruent trapeziums make a rectangle.
Examples
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Question
Identify the parallel sides and the height for this trapezium.
The parallel sides are 饾拻 and 饾挃. The parallel sides are a fixed distance apart throughout their length.
The height is the line labelled 饾挆. The height is the shortest distance between the parallel sides. The height is at right angles to the parallel sides.
Calculating the area of a trapezium
To calculate the area of a trapezium:
Identify the parallel sides 饾拏 and 饾拑, and the perpendicular height, 饾拤.
Substitute the values of 饾拏, 饾拑 and 饾拤 into the formula.
Complete the calculation. Remember that the result is an area so the units are square centimetres (cm虏).
Example
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Question
Work out the area of the trapezium.
- Identify the parallel sides 饾拏 and 饾拑, and the perpendicular height, 饾拤.
- The parallel sides are 10 mm and 4 mm.
- The height is at right angles to the parallel sides.
- The height is 6 mm.
- Substitute the values for 饾拏, 饾拑, and 饾拤 into the formula for the area of a trapezium.
- Complete the calculation.
陆 (10+4) 脳 6 = 42
The area of the trapezium is 42 mm虏
Practise finding the area of trapeziums
Practise finding the area of trapeziums with this quiz. You may need a pen and paper to help you with your answers.
Quiz
Real-life maths
Plasterers are skilled tradespeople who apply plaster and decorative finishes to walls and ceilings. Walls are covered with plaster so that further decoration goes onto a smooth surface.
An attic converted to a bedroom can have trapezium-shaped walls. The amount of plaster used depends on the area of the walls, so knowing how to work out the area of a trapezium is important. It will also impact on how much time a plasterer will need to finish the job and therefore how much it will cost overall.
Game - Divided Islands
Play the Divided Islands game! gamePlay the Divided Islands game!
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