How trapezoid area is calculated
A trapezoid's area is the average of its two parallel sides times the height between them.
A = (a + b) ÷ 2 × h
- Add the two parallel sides (bases a and b) and halve them. This is the median.
- Multiply the median by the height, measured straight across between the bases.
- To find the height: h = 2A ÷ (a + b).
- To find a missing base: b = 2A ÷ h − a.
- Perimeter is a + b + c + d, where c and d are the slanted legs. Each leg is at least as long as the height.
Worked example — Bases of 8 cm and 5 cm with a height of 4 cm: A = (8 + 5) ÷ 2 × 4 = 26 cm². The median is 6.5 cm.
Common trapezoid sizes
| Base a | Base b | Height | Measured in | Area |
|---|---|---|---|---|
| 8 cm | 5 cm | 4 cm | Centimetres | 26 cm² |
| 10 m | 6 m | 3 m | Metres | 24 m² |
| 12 in | 8 in | 5 in | Inches | 50 in² |
| 20 cm | 14 cm | 7 cm | Centimetres | 119 cm² |
| 3.5 m | 2 m | 1.5 m | Metres | 4.125 m² |
Swipe the table sideways to see the rest.
Base a, base b and height. Each row is worked out by this calculator.
Things to consider
- Measure the height at right angles to the bases, not along a slanted side.
- The two bases are the parallel sides. It does not matter which one you call a.
- For an odd-shaped garden bed, split it into trapezoids and rectangles and add the areas.
- Use the same unit for every measurement before you start.
Frequently asked questions
What is the formula for the area of a trapezoid?
A = (a + b) ÷ 2 × h, where a and b are the parallel sides and h is the height. Bases of 8 and 5 with height 4 give 26.
Is a trapezoid the same as a trapezium?
Yes, in everyday use. Australia and the UK say trapezium for a four-sided shape with one pair of parallel sides; the US says trapezoid. The formula is the same.
How do I find the height of a trapezoid?
Double the area and divide by the sum of the bases: h = 2A ÷ (a + b). An area of 26 with bases 8 and 5 gives a height of 4.
What is the median of a trapezoid?
The median, or midsegment, joins the midpoints of the legs. Its length is (a + b) ÷ 2, and area is the median times the height.
How do I find the perimeter of a trapezoid?
Add all four sides: a + b + c + d. Enter the two legs under the advanced options to see it.
Can I use this for a garden bed or roof section?
Yes. Any area with two parallel edges, such as a tapered garden bed or a hip roof face, is a trapezoid. Measure the height straight across.
Results are estimates for general information only, not financial, medical or professional advice.