Geometry desk
Trapezoid Area Calculator
Calculate a trapezoid's area from its two parallel bases and height.
Trapezoid Area Calculator: Find the surface inside a quadrilateral with two parallel bases, using those base lengths and the perpendicular gap between them. You can estimate a tapered panel's area without measuring its two sloping sides or treating it as a rectangle. Runs 100% locally in your browser with zero server file uploads.
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Area
55 cm²
Area = (base 1 + base 2) × height ÷ 2- Base 1 and base 2 are parallel.
- Dimensions are measured in the same unit.
- Values must be finite and greater than zero.
Formula and worked example
Area = (base 1 + base 2) × height ÷ 2
A worked example with sample values:
| Inputs | |
|---|---|
| Base 1 | 8 cm |
| Base 2 | 14 cm |
| Height | 5 cm |
| Results | |
|---|---|
| Area | 55 cm² |
Average width across the height
Let a and b be the parallel base lengths and h their perpendicular separation. Area A = (a + b) × h ÷ 2. Rotating a second identical trapezoid and placing it beside the first creates a parallelogram with base a + b and height h. One trapezoid therefore occupies half its area. Equivalently, multiply the average base length by the height.
For bases 8 cm and 14 cm with height 5 cm, add the bases to obtain 22 cm. Their average is 22 ÷ 2 = 11 cm. Multiply 11 × 5 = 55 cm². The calculator reports Area = 55 cm²; using only the longer base would incorrectly give 70 cm².
OpenStax includes the parallel-base area formula (https://openstax.org/books/prealgebra-2e/pages/9-4-use-properties-of-rectangles-triangles-and-trapezoids). This page uses the word trapezoid; the shape is also called a trapezium in British usage.
A missing height and a unit check
If area and both bases are known, solve h = 2A ÷ (a + b). Using 55 cm² with bases 8 and 14 cm gives h = 110 ÷ 22 = 5 cm. Area does not determine the sloping side lengths, because shifting the shorter base sideways can leave the same height. A 55 cm² result equals 0.0055 m², using the squared centimetre-to-metre factor. All three entries must be positive; a zero-length base would reduce the shape to a triangle and is outside this form's accepted inputs.
How to use it
- Enter positive dimensions in the same unit.
- Choose the unit used for every dimension.
- Calculate, then review the result and formula.
Privacy & limitations
Every value and calculation stays in your browser. No dimensions are uploaded or sent to an external service.
Related tools
Frequently asked questions
Which trapezoid sides should I use as bases?
Use the parallel pair, even if neither side is horizontal in your drawing. The other two sides are legs and do not belong in the base fields. Swapping the two parallel base entries leaves the area unchanged.
Can the sloping edge be used as trapezoid height?
Only if that edge is perpendicular to both bases. Normally height is the shortest distance between the parallel lines, so a sloping leg is longer and would produce too large an area.
What happens when both parallel bases are equal?
The formula becomes base × height, the parallelogram area rule. With two bases of 8 cm and a perpendicular height of 5 cm, the area is 40 cm², regardless of the sideways offset between them.
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