Key takeaways
- The area of a trapezoid is A = (a + b) × h ÷ 2.
- a and b are the two parallel sides; h is the perpendicular height between them.
- The formula averages the two parallel sides before multiplying by the height.
- If a and b become equal, the shape is really a parallelogram, and the formula still works.
In this guide
What is a trapezoid?
A trapezoid (also called a trapezium) is a four-sided shape with exactly one pair of parallel sides. Those parallel sides are usually called the two bases, and they can be different lengths.
Why does the area of a trapezoid matter?
Trapezoids show up whenever a shape narrows or widens on one side only — tables, lampshades, and irregular plots of land all use this exact formula.
If a trapezoid's two parallel sides happen to be equal — say both are 5 m, with a height of 4 m — the formula still works: (5 + 5) × 4 ÷ 2 = 20 m², which is exactly what you'd get from the rectangle or parallelogram formula for the same base and height.The formula
| Symbol | What it means | Example |
|---|---|---|
| A | The area you want to find | 15 m² |
| a | The length of the first parallel side (base) | 4 m |
| b | The length of the second parallel side (base) | 6 m |
| h | The perpendicular distance between the two parallel sides | 3 m |
How to find the area step by step
- 1Measure both parallel sides. These are your two bases, a and b.
- 2Add the two bases together.
- 3Measure the height. The straight-line distance between the two parallel sides.
- 4Multiply the sum of the bases by the height.
- 5Divide the result by 2.
Now try it yourself. Change the two bases and height in the calculator below and watch the area update, with every step shown.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Forgetting to divide by 2. The formula averages the two bases before multiplying by height, which is why the divide-by-2 step matters.
- Mixing up which sides are parallel. Only the two bases (a and b) go in the formula, not the slanted sides.
- Skipping the height entirely. Unlike area from three sides (Heron's formula), a trapezoid genuinely needs a perpendicular height measurement.
Tips and tricks
- Think of the formula as "average the two bases, then treat it like a rectangle":
((a + b) ÷ 2) × h. - If both parallel sides are equal, you're really working with a parallelogram or rectangle.
Where you'll use it in real life
- Gardening: working out the area of a trapezoid-shaped garden bed.
- Interior design: calculating fabric for a lampshade panel.
- Land surveying: estimating land area for an irregularly shaped plot.
- Woodworking: sizing a tapered tabletop or shelf.
Quick summary
To find the area of a trapezoid, add the two parallel sides, multiply by the height, and divide by 2. The height must always be perpendicular to the parallel sides. Use the calculator above to check your own trapezoid instantly.
Worked example
You're building a raised garden bed shaped like a trapezoid, with parallel sides of 4 meters and 6 meters, and a height of 3 meters between them. How much ground space does it cover?
- 01A = (a + b) × h ÷ 2
- 02A = (4 + 6) × 3 ÷ 2
- 03A = 10 × 3 ÷ 2
- 04A = 30 ÷ 2
- 05A = 15 m²
These numbers are pre-filled in the calculator above.
Frequently asked questions
How do I find the area of a trapezoid if I don't know the height?
You need the perpendicular height between the two parallel sides; it can't be skipped. If you know the slanted sides and bases, you can often find the height using the Pythagorean theorem.
What's the difference between a trapezoid and a parallelogram?
A trapezoid has only one pair of parallel sides; a [parallelogram](/calculator/area-parallelogram) has two pairs. This is why their area formulas look different.
Does it matter which base I call 'a' and which I call 'b'?
No. Since the formula adds a and b together, it doesn't matter which parallel side you label first.
What happens if both parallel sides of a trapezoid are equal?
Then it isn't really a trapezoid anymore, it's a parallelogram, and the same formula still works because (a + b) ÷ 2 just becomes the shared base length.
