This trapezoid calculator finds a trapezoid’s area, perimeter and midline from its two parallel sides, height and legs — and can recover the height from the sides alone when all four are known.
Area = midline × height — the trapezoid is secretly a rectangle in disguise: slice it along the midline, flip the top half, and the two bases merge into one side of length (a + b)/2. (In British usage this shape is a “trapezium” and an American trapezium has no parallel sides at all — the Atlantic’s cruelest geometry joke; the math here is for one pair of parallel sides.)
Area = Average of the Bases × Height
A = (a + b)/2 × h — the formula reads as “the width halfway up, times the height,” which is exactly what the midline (median) is: the segment joining the leg midpoints, length (a + b)/2. The same average-of-extremes idea powers the trapezoid rule in calculus for approximating integrals. Its triangular kin: our Triangle Calculator. Part of our Math Calculators collection.
Worked Example (Verified)
- Bases 10 and 4, height 4, legs 5 and 5 (defaults, an isosceles trapezoid): area = 7 × 4 = 28 · perimeter = 24 · midline = 7
- Height recovery check: blank the height field and the projection formula reconstructs it — each leg overhangs (10−4)/2 = 3, so h = √(5² − 3²) = √16 = 4 exactly, confirming the four sides and the height agree.
- Land-plot reality: a lot 30 m × 22 m across and 18 m deep → (30+22)/2 × 18 = 468 m² — the surveyor’s everyday use
- The midline is also the average-value width: any linear taper (a tapered garden bed, a frustum’s face) prices material by midline × length
Definitions Worth Pinning Down
- US: trapezoid = at least one pair of parallel sides (inclusive) or exactly one pair (exclusive) — textbooks war over it; parallelograms are the disputed border.
- Isosceles trapezoid: legs equal, base angles equal, diagonals equal — the symmetric case most problem sets quietly assume.
- Right trapezoid: two right angles — a rectangle with one slanted side, common in ramps and roof sections.
Related Tools
- Triangle Calculator — the three-sided foundation
- Area Calculator — every common shape
- Math Calculators — the full collection
Frequently Asked Questions
How do you find the area of a trapezoid?
A = (a + b) ÷ 2 × h — the average of the two parallel sides times the perpendicular height. Bases 10 and 4 with height 4 give 28 square units. Equivalently: midline length × height.
What is the midline (median) of a trapezoid?
The segment joining the midpoints of the two legs; its length is the average of the bases, (a + b)/2. It splits the trapezoid into two smaller trapezoids of equal height, and area = midline × height follows immediately.
Can I find the height from the four sides?
Yes — project the legs onto the base difference: the geometry reduces to two right triangles sharing the height. This calculator does it when the height field is empty and both legs are given (the result appears in the “Height Used” card).
Is a parallelogram a trapezoid?
Depends on the definition in force: inclusive definitions (at least one parallel pair) say yes; exclusive ones (exactly one pair) say no. The area formula works either way — with a = b it degenerates gracefully to base × height.
Trapezoid vs trapezium?
American English: trapezoid has a pair of parallel sides; trapezium has none. British English historically swaps the two. When reading international sources, trust the diagram, not the word — this page’s shape is the one-pair-of-parallel-sides figure.
Is this trapezoid calculator free?
Yes — free, instant, no sign-up.