Area of a Trapezium: Formula, Diagram and Worked Examples
Use the two parallel sides and perpendicular height to find trapezium area, with a visual explanation of why the formula works.
The formula
Here, a and b are the lengths of the parallel sides, and h is the perpendicular distance between them.
Worked example
Area = 66 cm².
Why the formula works
The average length of the two parallel sides is (a+b)/2. Multiplying that average width by the height gives the same area as the trapezium. Another way to see it is that two matching trapeziums can be paired to form a parallelogram with base a+b and height h; one trapezium is half of that area.
Which height counts?
A sloping side is not the height unless it meets the parallel sides at 90°. If a diagram gives a slanted edge and a separate perpendicular line, use the perpendicular line.
What to inspect on the diagram before substituting
- Adding non-parallel sides in the formula.
- Forgetting the factor of ½.
- Using cm instead of cm² for area.
Does the area fit the shape?
The average of 8 and 14 is 11, so the shape should have about the same area as an 11-by-6 rectangle: 66 cm². That matches.
A trapezium has parallel sides 10 and 16, height 5. What is its area?
Keep going
For another problem using related ideas, return to the Geometry & Mensuration page.