# What is the area of my trapezoid?

Computes a trapezoid’s area, midsegment and perimeter from its bases and height, or its height, area and angles from all four sides.

- Page: https://www.acalculator.org/math/trapezoid-calculator
- JSON spec: https://www.acalculator.org/math/trapezoid-calculator.json
- Version: 3f5fbc75184d

## Default answer

Example with the default inputs (I know Bases and height, Base a (bottom) 10, Base b (top) 4, Height h 4): A trapezoid with bases 10 and 4 and height 4 has an area of 28.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| mode | I know | Whether you know the two bases and the height, or all four sides. |
| a | Base a (bottom) | The length of one of the two parallel sides. |
| b | Base b (top) | The length of the other parallel side. |
| h | Height h | The distance between the two bases, at right angles to them. |
| c | Leg c (left) | The side that joins the left ends of the bases. |
| d | Leg d (right) | The side that joins the right ends of the bases. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| area | Area | Half the sum of the bases times the height: (a + b) ÷ 2 × h. |
| median | Midsegment | The line joining the midpoints of the legs: (a + b) ÷ 2. |
| perimeter | Perimeter | The sum of the four sides: a + b + c + d. |
| height | Height | The distance between the bases. |
| angleA | Angle between a and c | The inside angle where base a meets leg c, in degrees. |
| angleB | Angle between a and d | The inside angle where base a meets leg d, in degrees. |
| angleC | Angle between b and c | The inside angle where base b meets leg c: 180° minus the angle at a and c. |
| angleD | Angle between b and d | The inside angle where base b meets leg d: 180° minus the angle at a and d. |

## Method

Area = (a + b) ÷ 2 × h; midsegment = (a + b) ÷ 2; perimeter = a + b + c + d; from four sides: x = (c² − d² + (a − b)²) ÷ (2(a − b)), h = √(c² − x²).

## Assumptions

- a and b are the parallel sides (bases); c joins their left ends and d their right ends.
- All lengths are in the same unit; the area is in that unit squared.

## Worked examples

1. mode = height, a = 14, b = 11, h = 6 gives area = 75, median = 12.5. Source: OpenStax, Prealgebra 2e, §9.4 Use Properties of Rectangles, Triangles, and Trapezoids, Example 9.38 (A = ½h(b + B): height 6, bases 14 and 11, area 75). https://openstax.org/books/prealgebra-2e/pages/9-4-use-properties-of-rectangles-triangles-and-trapezoids.
2. mode = height, a = 8.2, b = 5.6, h = 3.4 gives area = 23.46, median = 6.9. Source: OpenStax, Prealgebra 2e, §9.4, Example 9.40 (height 3.4 yd, bases 8.2 and 5.6 yd: 23.46 square yards). https://openstax.org/books/prealgebra-2e/pages/9-4-use-properties-of-rectangles-triangles-and-trapezoids.
3. mode = sides, a = 10, b = 4, c = 5, d = 5 gives height = 4, area = 28, perimeter = 24, angleA = 53.130102, angleC = 126.869898. Source: OpenStax, Prealgebra 2e, §9.4 (area of a trapezoid) and §9.3 (Pythagorean theorem). https://openstax.org/books/prealgebra-2e/pages/9-4-use-properties-of-rectangles-triangles-and-trapezoids.
4. mode = sides, a = 7, b = 3, c = 3, d = 5 gives height = 3, area = 15, angleA = 90, angleB = 36.869898. Source: OpenStax, Prealgebra 2e, §9.4 (area of a trapezoid) and §9.3 (Pythagorean theorem). https://openstax.org/books/prealgebra-2e/pages/9-4-use-properties-of-rectangles-triangles-and-trapezoids.
5. mode = height, a = 10, b = 4, h = 4, c = 5, d = 5 gives area = 28, perimeter = 24. Source: OpenStax, Prealgebra 2e, §9.4 Use Properties of Rectangles, Triangles, and Trapezoids. https://openstax.org/books/prealgebra-2e/pages/9-4-use-properties-of-rectangles-triangles-and-trapezoids.

## FAQ

### What is the formula for the area of a trapezoid?

Area = (a + b) ÷ 2 × h, where a and b are the parallel sides (the bases) and h is the height between them. A trapezoid with bases 14 and 11 and height 6 has an area of (14 + 11) ÷ 2 × 6 = 75.

### How do I find the height of a trapezoid from its sides?

Slide the two legs together to form a triangle with sides c, d and a − b. Its height is the trapezoid’s height. In numbers, x = (c² − d² + (a − b)²) ÷ (2(a − b)) and h = √(c² − x²). For bases 10 and 4 and legs 5 and 5: x = 3 and h = 4.

### What is the midsegment of a trapezoid?

The midsegment (or median) joins the midpoints of the two legs. It is parallel to the bases and its length is their average, (a + b) ÷ 2. The area is the midsegment times the height.

### Why can I not find the height when the bases are equal?

Equal parallel sides make a parallelogram, which can lean by any amount with the same four sides. The sides do not fix its height, so the page asks for the height instead.

### How do I find the perimeter of a trapezoid?

Add all four sides: a + b + c + d. In "Bases and height" mode, type both legs to see it; the page checks that the legs fit the bases and the height.

### Is a trapezium the same as a trapezoid?

In British English a trapezium is a four-sided shape with one pair of parallel sides, which is what American English calls a trapezoid. The formulas are the same.

## Sources

- OpenStax, Prealgebra 2e, §9.4 Use Properties of Rectangles, Triangles, and Trapezoids (area of a trapezoid A = ½h(b + B); Examples 9.38 and 9.40). https://openstax.org/books/prealgebra-2e/pages/9-4-use-properties-of-rectangles-triangles-and-trapezoids (retrieved 2026-10-01)
- OpenStax, Prealgebra 2e, §9.3 Use Properties of Angles, Triangles, and the Pythagorean Theorem. https://openstax.org/books/prealgebra-2e/pages/9-3-use-properties-of-angles-triangles-and-the-pythagorean-theorem (retrieved 2026-10-01)