What is the area formula for a trapezoid?

Area equals one-half times the sum of the two parallel bases times the height (A = 1/2 · (a + b) · h).

What is the midsegment of a trapezoid?

The midsegment, or median, equals the average of the two parallel bases, (a + b) / 2.

Why do the legs only change the perimeter?

The area depends only on the two parallel bases and the height. The legs affect the perimeter but not the enclosed area.

What is the difference between a trapezoid and a trapezium?

They are the same four-sided shape with one pair of parallel sides. Trapezoid is the US term and trapezium the British term; this calculator works for either name.

How is the perimeter calculated?

The perimeter is the sum of all four sides: the two parallel bases plus the two legs (a + b + c + d).

Does the height have to be perpendicular?

Yes. The height is the perpendicular distance between the two parallel bases, not the length of a slanted leg, since the area formula relies on the perpendicular height.

Yes, as long as all lengths use the same unit. The area then comes out in that unit squared and the perimeter and midsegment in the same linear unit.

What is the Trapezoid Calculator?

Free trapezoid calculator — enter the two parallel bases, height and legs to get area, perimeter and the midsegment. Runs entirely in your browser, nothing is uploaded. It runs free in your browser on Gera Tools, with nothing uploaded.

Trapezoid Calculator

Name: Trapezoid Calculator
Creator: Gera Tools
License: https://creativecommons.org/licenses/by/4.0/

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Trapezoid calculator

A trapezoid (British: trapezium) is a four-sided shape with one pair of parallel sides, called the bases. This calculator finds its area, midsegment, and perimeter from the bases, the height, and the two legs — useful for geometry homework, construction layouts, and land-area estimates.

How it works

Let the parallel bases be a (top, shorter) and b (bottom, longer), the perpendicular height be h, and the two slanted legs be c and d:

Area       = ½ × (a + b) × h
Midsegment = (a + b) / 2
Perimeter  = a + b + c + d

The area formula averages the two bases — intuitively, a trapezoid is like a rectangle whose top has been slid or shortened. The midsegment is the segment connecting the midpoints of the two legs; its length equals exactly that average. The legs affect the perimeter but not the area, because area depends only on the cross-sectional width (averaged) and the height.

Height vs. leg length: the most common mistake is entering the slant leg length as the height. The height h must be the perpendicular (right-angle) drop from the top base to the bottom base. For a right trapezoid one leg is already vertical, so that leg length equals the height. For an oblique trapezoid you may need to use trigonometry (h = leg × sin(angle)) to find the true perpendicular height before entering it here.

Worked example

For bases a = 8 m and b = 12 m, height h = 5 m, and legs c = 6 m, d = 7 m:

Area = ½ × (8 + 12) × 5 = ½ × 20 × 5 = 50 m²
Midsegment = (8 + 12) / 2 = 10 m
Perimeter = 8 + 12 + 6 + 7 = 33 m

Quantity	Value	Unit
Area	50	m²
Midsegment	10	m
Perimeter	33	m

Special cases worth knowing

Parallelogram: when both bases are equal (a = b) the trapezoid becomes a parallelogram. Area simplifies to base × height and the midsegment equals either base.
Rectangle: a parallelogram with right-angle legs. Here legs = height.
Isosceles trapezoid: both legs are equal (c = d). The shape is symmetric; the diagonals are equal in length.
Right trapezoid: one leg is perpendicular to both bases, making that leg equal to the height.

Practical uses

Land surveyors frequently encounter trapezoidal plots — a road frontage wider than the rear boundary, for example. Architects use the trapezoid area formula for sloped roof cross-sections and retaining-wall footprints. In sheet-metal work, a trapezoidal duct cross-section requires both area (for flow calculations) and perimeter (for material length). Use the same unit for all inputs; the area result will be in that unit squared automatically.