Calculations at a trapezoid. A trapezoid (or trapezium) is a tetragon with two parellel sides.
Enter three side lengths and one angle between two of those sides. Choose the number of decimal places and click Calculate. Please enter angles in degrees, here you can convert angle units. Only those trapezoids can be calculated here, where c doesn't overlap a (g1, g2 ≥ 0; α, β ≤ 90°), for others see obtuse trapezoid.
Example for a trapezoid: a=4, b=3, c=2.5, β=80°

Trapezoid shape:

Formulas:
α + δ = 180°
β + γ = 180°
a = c + g_{1} + g_{2}
g_{1} = √ d² - h²
g_{2} = √ b² - h²
α = arccos( (g_{1}²+d²-h²) / ( 2*g_{1}*d ) )
β = arccos( (g_{2}²+b²-h²) / ( 2*g_{2}*b ) )
h = b * sin(β) = b * sin(γ) = d * sin(α) = d * sin(δ)
e = √ a² + b² - 2ab*cos(β)
f = √ a² + d² - 2ad*cos(α)
m = ( a + c ) / 2
p = a + b + c + d
A = ( a + c ) / 2 * h

Side lengths, height, diagonals and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).

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perimeter p, area A

sides and angles

height

diagonals

central median

A special form of trapezoid is the parallelogram, in which not just one pair, but both pairs of opposite sides are parallel to each other. Another special case is the obtuse trapezoid, which the calculator on this page cannot calculate. There are also right trapezoids, isosceles trapezoids and tri-equilateral trapezoids. The rectangle, the rhombus and the square are also trapezoids.
In old writings from the beginning of the 20th century and before, the term trapezoid was generally used for general quadrilaterals or specifically those without parallel sides. Trapezoids in the modern sense were called parallel trapezoids. This can be confusing when reading such writings these days. The name of the three-dimensional shape trapezohedron goes back to the old meaning of the word trapezoid.
The general trapezoid has no symmetries, an isosceles trapezoid has an axis of symmetry through the middle of the two parallel sides.