Calculations in 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°).
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).