Complete trapezoid calculator. Enter parallel sides, height, and optional legs for area, perimeter, midsegment, diagonals, and angles. Supports right, isosceles, and general trapezoids.
A trapezoid, called a trapezium in some regions, is a quadrilateral with one pair of parallel sides. Those parallel sides are the bases, and the perpendicular distance between them is the height. The other two sides are the legs. This shape shows up in roof lines, bridge sections, buckets, channels, retaining walls, and many land-area sketches where the top and bottom edges are parallel but different in length.
Its core area formula is simple: A = ½(a + b) × h. In words, the area is the average of the two bases multiplied by the height. That same average base length is the midsegment, so the trapezoid is one of the clearest examples of how an average measurement can become a direct geometric quantity.
Different subclasses add more structure. In an isosceles trapezoid, the legs match, the base angles match in pairs, and the diagonals are equal. In a right trapezoid, one leg is perpendicular to the bases, so two angles are exactly 90°. A general trapezoid has no such symmetry, which is why diagonal and angle calculations usually rely on a coordinate model.
This calculator handles all three cases. Enter the bases and height, then add leg information when the selected type requires it. The results include area, perimeter, midsegment, both diagonals, all four interior angles, comparison bars, and a property table so you can move from a rough sketch to a complete geometric summary.
This calculator is useful because trapezoid problems rarely stop at area. In practical geometry and design work, you often need perimeter for material estimates, diagonals for bracing or layout checks, and angles for cuts or drafting. Once the trapezoid type changes from isosceles to right or general, the relationships are no longer interchangeable, so using a tool that respects the chosen geometry saves time and avoids incorrect assumptions.
It is also helpful for teaching because it makes the contrasts between trapezoid families explicit. You can see when equal diagonals are a real property, when a leg matches the height, and how changing one base affects the midsegment and angles even if the area stays close.
Area: A = ½(a + b) × h Midsegment: m = (a + b) / 2 Perimeter: P = a + b + leg₁ + leg₂ Right trapezoid slanted leg: c = √(h² + (b − a)²) when the other leg equals h Isosceles trapezoid diagonal: d = √(leg² + ab) Isosceles leg from height: leg = √(h² + ((b − a)/2)²) Coordinate model for general trapezoid: place the bottom base on the x-axis and use the distance formula for diagonals and angles
Result: Area = 32, perimeter ≈ 24.94, midsegment = 8, legs ≈ 4.47, diagonals ≈ 8.94
For an isosceles trapezoid with bases 6 and 10 and height 4, the horizontal offset on each side is (10 − 6) / 2 = 2. Each leg is therefore √(4² + 2²) = √20 ≈ 4.47. The area is ½(6 + 10) × 4 = 32, the midsegment is (6 + 10) / 2 = 8, the perimeter is 6 + 10 + 2(4.47) ≈ 24.94, and each diagonal is √(4.47² + 6×10) = √80 ≈ 8.94.
The trapezoid midsegment is more than a secondary property. Because its length is exactly the average of the two bases, the area formula can be read as midsegment × height. That makes the midsegment the cleanest way to think about how a trapezoid balances a short base and a long base into one effective width. If you understand that idea, the area formula becomes intuitive instead of memorized.
An isosceles trapezoid adds symmetry: equal legs, equal base angles, and equal diagonals. A right trapezoid adds perpendicular structure, which immediately fixes two angles and one leg-height relationship. A general trapezoid has neither shortcut, so diagonal and angle values depend on how the top base is horizontally positioned relative to the bottom base. Treating all three with the same formula set is a common mistake, and that is exactly why the type selector matters.
Trapezoids show up whenever two edges stay parallel while the side boundaries taper. Roof sections, drainage channels, retaining walls, tabletops, and lot sketches often reduce to trapezoid geometry. In those settings, area alone is not enough; you may also need diagonal lengths for bracing, side lengths for trim, or angle values for cuts. The calculator helps connect the simple textbook area rule to those more realistic measurement tasks.
Area = ½ × (base₁ + base₂) × height. This is equivalent to the midsegment times the height.
The segment connecting the midpoints of the two legs. Its length = (a + b) / 2, the average of the parallel sides.
A trapezoid with both legs of equal length. Its base angles are equal and its diagonals are equal.
A trapezoid where one leg is perpendicular to both bases. It has two right angles (90°).
Use coordinate geometry or the formula d = √(leg² + a·b) for an isosceles trapezoid. For general trapezoids, place the shape on a coordinate plane and apply the distance formula.
Under the inclusive definition, yes (it has at least one pair of parallel sides). Under the exclusive definition used in many textbooks, no — a parallelogram has two pairs.