What is a trapezoid?
A trapezoid (also called a trapezium in British English) is a quadrilateral — a four-sided polygon — that has at least one pair of parallel sides. The two parallel sides are called bases (usually labeled a for the bottom base and b for the top base), while the other two non-parallel sides are called legs (labeled c and d).
Note: In the American definition, a trapezoid has exactly one pair of parallel sides. The British definition (trapezium) allows for at least one pair, so a parallelogram and rectangle are special trapezoids.
Special types of trapezoids
Isosceles trapezoid
An isosceles trapezoid has two equal legs (c = d). The base angles are equal, and the diagonals have the same length. Our calculator handles this case automatically when you enter equal leg lengths.
Right trapezoid
A right trapezoid has one leg perpendicular to both bases (one of the base angles equals 90°). In this case, the leg length equals the height of the trapezoid.
Scalene trapezoid
A scalene trapezoid has legs of different lengths and no special symmetry. This is the general case computed by default.
Trapezoid perimeter formula
The perimeter is simply the sum of all four sides:
P = a + b + c + d
where a and b are the parallel bases, and c and d are the legs.
How to calculate the area of a trapezoid
The area of a trapezoid is calculated using the average of the two bases multiplied by the height:
A = (a + b) / 2 × h
This formula works because a trapezoid can be seen as a rectangle with two triangles cut from the sides — averaging the bases gives the effective width, and multiplying by height gives the area.
How to find the height of a trapezoid
Given all four sides (a, b, c, d), the height can be derived geometrically. Place the trapezoid on a coordinate system with the bottom base along the x-axis. The horizontal offset x of the left leg satisfies:
x = ((a − b)² + c² − d²) / (2 × (a − b))
Then the height is:
h = √(c² − x²)
For an isosceles trapezoid (c = d), this simplifies to:
h = √(c² − ((a − b) / 2)²)
Trapezoid angles
The four interior angles of a trapezoid always sum to 360°. Because the bases are parallel, co-interior (same-side interior) angles are supplementary:
- α + γ = 180° (left base angle + left top angle)
- β + δ = 180° (right base angle + right top angle)
The base angles α and β are computed as:
α = arctan(h / x) β = arctan(h / (a − b − x))
Median of a trapezoid
The median (also called the midsegment) connects the midpoints of the two legs. It is always parallel to the bases and its length equals the arithmetic mean of the two bases:
m = (a + b) / 2
Note that this is the same value used in the area formula, which explains why A = m × h.
Diagonals of a trapezoid
A trapezoid has two diagonals. In general, they have different lengths. For an isosceles trapezoid, the diagonals are equal. Our calculator outputs both diagonal lengths p and q.
Unit systems supported
This calculator supports both metric (mm, cm, m, km) and US imperial (in, ft, yd, mi) units. Select your unit in the dropdown before entering the side lengths. The area is returned in square units (e.g., cm²), while all linear results (perimeter, height, median, diagonals) are in the selected unit.
Example: using the trapezoid calculator
Suppose you have a trapezoid with:
- Bottom base a = 10 cm
- Top base b = 6 cm
- Left leg c = 5 cm
- Right leg d = 5 cm (isosceles)
Step 1 — Height: h = √(5² − ((10 − 6) / 2)²) = √(25 − 4) = √21 ≈ 4.583 cm
Step 2 — Area: A = (10 + 6) / 2 × 4.583 = 8 × 4.583 ≈ 36.66 cm²
Step 3 — Perimeter: P = 10 + 6 + 5 + 5 = 26 cm
Step 4 — Median: m = (10 + 6) / 2 = 8 cm
Step 5 — Angles: α = β = arctan(4.583 / 2) ≈ 66.42°; γ = δ ≈ 113.58°
FAQs
What is the difference between a trapezoid and a parallelogram?
A parallelogram has two pairs of parallel sides. A trapezoid (US definition) has exactly one pair. Our calculator requires the bases to be different lengths (a ≠ b); equal bases would make it a parallelogram, which needs a different approach.
Can the legs be longer than the bases?
Yes — as long as the four sides form a valid trapezoid (the height computed from the sides is a real positive number). The calculator will display an error if the entered dimensions are geometrically impossible.
What if my trapezoid is a right trapezoid?
Enter the legs so that one leg equals the height (the other leg and bases determine the rest). The calculator will compute angle α = 90° automatically when the geometry dictates it.
Does this calculator work with imperial units?
Yes. Select inches, feet, yards, or miles from the unit dropdown. All results will be in the chosen unit (and square unit for area).