Trapezoid area is one of 3 quadrilaterals formulas in the geometry section of this library, and it is used at middle school level.
Why trapezoid area works
Place a second, upside-down copy of the trapezoid beside the first and the two fit together into a parallelogram. Its base is the two parallel sides added together and its height is unchanged, so a single trapezoid covers half of that, which is why the two parallel sides get averaged.
What each symbol means
$b_1,b_2$ are parallel side lengths and $h$ is perpendicular distance between them.
Trapezoid area: when it holds
The identified bases must be parallel.
When it stops applying
The two sides being averaged must genuinely be parallel. A quadrilateral with no parallel pair is not covered at all, and it has to be cut along a diagonal into two triangles that are measured separately.
Trapezoid area: a worked example
Bases $5,11$ and height $3$ give $A=24$.
The mistake to avoid
What people do: Averaging all four sides rather than only the two parallel ones.
Why it goes wrong: The slanted legs play no part in this measurement, and folding them into the average mixes in lengths that do not stretch across the shape.
Do this instead: Pick out the two parallel sides, average only those, and multiply by the distance between them.
Trapezoid area: step by step
- Name the unknown, and the unit the answer has to come out in.
- Match the symbols to your values. $b_1,b_2$ are parallel side lengths and $h$ is perpendicular distance between them.
- Check the conditions before substituting. The identified bases must be parallel.
- Substitute, keep exact values to the last line, then test the sign, size, and unit against a rough estimate — the check that catches most geometry slips.
Where this formula fits
- Subject
- Geometry formulas — 30 entries in this library
- Topic
- Quadrilaterals
- Level
- Middle school
Formulas are easiest to keep when they sit inside a method rather than on a list. Use the links below to see where trapezoid area comes from, to check a calculation against a tool, and to practise it until you can recall it without looking.
- Area of a Triangle — the lesson behind this formula: choose a base-height, trigonometric, or side-length formula.
- Geometry Calculator — check your substitution and the value it produces.
- Study geometry — the subject guide that explains the ideas these formulas compress.
- Geometry Practice — questions that make you retrieve the formula instead of recognising it.
- All 30 geometry formulas — the full grouped reference, or the complete formula library.
Questions about trapezoid area
What if the longer parallel side is on top?
It makes no difference at all. Addition does not care about order, so the average of the two parallel sides is unchanged.
Why is the average of the bases the right width to use?
The shape widens steadily from one parallel side to the other, so the width halfway up is exactly the average of the two, and that is the width a rectangle would need.
Does it reduce correctly for a rectangle?
Yes. Both parallel sides are then equal, their average is that same length, and the formula collapses to length times height.
How do I get the height when only the slanted legs are known?
Drop a perpendicular from an upper corner and use the Pythagorean theorem inside the small right triangle that this creates.