About

Miscalculating the area of a trapezoid leads to material waste in construction, incorrect land valuations, and flawed engineering designs. The standard formula A = 12 × (a + b) × h requires the perpendicular height between the two parallel sides, not a slant leg. Confusing the two is a common source of error that compounds in multi-step calculations such as cross-sectional volume estimates for channels and roadbeds. This tool validates inputs, computes area alongside perimeter, median, and approximate diagonals, and renders a proportional diagram so you can visually verify your geometry before committing to a design.

The calculator assumes a simple (non-self-intersecting) trapezoid with exactly one pair of parallel sides (a and b). For right trapezoids, one leg equals the height. For isosceles trapezoids, both legs are equal. Results approximate to four decimal places. Note: diagonal formulas assume a planar Euclidean trapezoid and require leg lengths in addition to parallel sides and height.

Formulas

The area of a trapezoid is derived from the average of its two parallel sides multiplied by the perpendicular distance between them:

A = 12 ⋅ (a + b) ⋅ h

Where a = length of the shorter parallel side (top base), b = length of the longer parallel side (bottom base), h = perpendicular height between the parallel sides.

The midsegment (median) connects the midpoints of the two non-parallel sides:

m = a + b2

This allows a compact restatement: A = m ⋅ h.

The perimeter requires all four sides:

P = a + b + c + d

Where c and d are the non-parallel legs. If only h is known (not the legs), the perimeter cannot be determined without additional data.

Diagonals of a trapezoid with known sides a, b, c, d:

p = √a² ⋅ d − b² ⋅ c + c ⋅ d ⋅ (c + d) ÷ √c + d

For the isosceles trapezoid (c = d), the diagonal simplifies to:

p = √a ⋅ b + c²

Reference Data

Trapezoid Type	Defining Property	Symmetry	Diagonal Relationship	Example Use Case
General (Scalene)	One pair of parallel sides, no equal legs	None	d₁ ≠ d₂	Irregular land plots
Isosceles	Non-parallel sides (legs) are equal	1 axis	d₁ = d₂	Architectural facades
Right	Two adjacent right angles	None	d₁ ≠ d₂	Staircase profiles, retaining walls
Parallelogram (special case)	Both pairs of sides parallel	2 axes	d₁ ≠ d₂ (unless rectangle)	Floor tiles, brickwork
Rectangle (degenerate)	a = b, all right angles	4 axes	d₁ = d₂	Window frames, rooms
Common Reference Areas
Trapezoid cross-section of a channel	a = 2 m, b = 4 m, h = 1.5 m		A = 4.5 m²
Highway embankment section	a = 8 m, b = 12 m, h = 3 m		A = 30 m²
Roof gable end	a = 3 m, b = 6 m, h = 2.5 m		A = 11.25 m²
Window trapezoid	a = 0.6 m, b = 0.9 m, h = 1.2 m		A = 0.9 m²
Small garden bed	a = 1 m, b = 1.8 m, h = 2 m		A = 2.8 m²
Unit Conversion Factors (Area)
1 m²	= 10,000 cm² = 10.7639 ft² = 1,550.0031 in²
1 ft²	= 929.0304 cm² = 0.0929 m² = 144 in²
1 yd²	= 9 ft² = 0.8361 m²
1 in²	= 6.4516 cm² = 645.16 mm²

Frequently Asked Questions

The height h is the perpendicular distance between the two parallel sides. A leg is a non-parallel side connecting the endpoints of the bases. They are only equal in a right trapezoid where one leg is perpendicular to both bases. In all other cases, the leg is longer than the height. Using a leg length in place of h will overestimate the area.

Yes. When a = b, the trapezoid degenerates into a parallelogram (or rectangle). The formula A = 12(a + b) ⋅ h reduces to A = a ⋅ h, which is the standard parallelogram formula. The calculator handles this correctly.

For a trapezoid with parallel sides a and b (where b > a) and legs c and d, drop perpendiculars from the top vertices to the bottom base. The horizontal offset x satisfies x = (b − a + c² − d²) ÷ (2(b − a)). Then h = √c² − x². The calculator performs this automatically when you enter all four sides.

The cross-sectional area formula remains the same. To get the volume of a trapezoidal prism (e.g., an irrigation channel), multiply the trapezoid area by the length L of the prism: V = A ⋅ L. This calculator gives you A; multiply by L manually for volume.

For residential construction, measure to the nearest 1 mm (0.001 m). For landscaping and earthwork, 1 cm is sufficient. The calculator displays up to 4 decimal places. Round your final answer according to the precision of your least-precise input measurement, per standard significant-figures rules.

If you manually enter two different leg values, the calculator treats it as a general (scalene) trapezoid. For an isosceles trapezoid, both legs must be identical. Enter the same value for c and d. The calculator will then recognize the symmetry and display matching diagonal lengths.