# Trapezoid Calculator

Calculate trapezoid area, perimeter, and median from bases and height. Supports isosceles and scalene trapezoids. Free online trapezoid calculator.

## What this calculates

Calculate the area, perimeter, and median of any trapezoid. Enter the two parallel bases and the height, with optional leg lengths for exact perimeter calculation.

## Inputs

- **Base 1 (longer parallel side)** — The longer parallel side of the trapezoid.
- **Base 2 (shorter parallel side)** — The shorter parallel side of the trapezoid.
- **Height** — The perpendicular distance between the two parallel sides.
- **Side A (left leg, optional)** — The left non-parallel side. If omitted, perimeter uses calculated slant.
- **Side B (right leg, optional)** — The right non-parallel side.

## Outputs

- **Area** — The area of the trapezoid: 1/2 x (b1 + b2) x h.
- **Perimeter** — The total length of all four sides.
- **Median (Midsegment)** — The segment connecting the midpoints of the legs: (b1 + b2) / 2.
- **Details** — formatted as text — Additional information about the trapezoid.

## Details

A trapezoid (trapezium in British English) is a quadrilateral with exactly one pair of parallel sides, called bases. The non-parallel sides are called legs.

Trapezoid Formulas

- Area: A = 1/2 x (b1 + b2) x h, where b1 and b2 are the parallel bases and h is the height.

- Median (Midsegment): m = (b1 + b2) / 2, which is the average of the two bases.

- Perimeter: P = b1 + b2 + leg1 + leg2.

Special Types

- Isosceles trapezoid: The legs are equal in length. Base angles are equal, and diagonals are equal.

- Right trapezoid: One leg is perpendicular to the bases, forming two right angles.

The area formula can be understood as the height times the average of the two bases, or equivalently, the height times the median.

## Frequently Asked Questions

**Q: How do I calculate the area of a trapezoid?**

A: Use the formula A = 1/2 x (b1 + b2) x h, where b1 and b2 are the lengths of the two parallel sides (bases) and h is the perpendicular distance between them. For example, with bases 8 and 12 and height 5: A = 1/2 x (8 + 12) x 5 = 1/2 x 20 x 5 = 50 square units.

**Q: What is the median of a trapezoid?**

A: The median (or midsegment) of a trapezoid is a segment connecting the midpoints of the two legs. Its length equals the average of the two bases: m = (b1 + b2) / 2. The median is parallel to both bases. Interestingly, the area can also be expressed as A = median x height.

**Q: What is an isosceles trapezoid?**

A: An isosceles trapezoid has legs of equal length. This means the base angles are equal, the diagonals are equal in length, and the trapezoid is symmetric about a perpendicular axis through the midpoints of both bases. Many real-world trapezoids, like bucket cross-sections, are isosceles.

**Q: Is a parallelogram a trapezoid?**

A: It depends on the definition. Under the inclusive definition, a parallelogram is a special trapezoid with two pairs of parallel sides. Under the exclusive definition (used in some countries), a trapezoid has exactly one pair of parallel sides, excluding parallelograms. Most modern textbooks use the inclusive definition.

**Q: How do I find the height of a trapezoid from the area?**

A: Rearrange the area formula: h = 2A / (b1 + b2). For example, if the area is 60 square units and the bases are 8 and 12: h = 2 x 60 / (8 + 12) = 120 / 20 = 6 units.

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Source: https://vastcalc.com/calculators/math/trapezoid
Category: Math
Last updated: 2026-04-21