Calculations at an obtuse trapezoid. An obtuse trapezoid is a trapezoid in which the oblique sides are either both inclined to the left or both to the right. Here, trapezoids inclined to the right (α and γ < 90°, β and δ > 90°) can be calculated. Trapezoids inclined to the left, please just flip vertically (swap a and c, α and δ, as well as β and γ). 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.
Example values for an obtuse trapezoid: a=4, b=2.7, d=2.8, α=72°
Obtuse trapezoid shape:
Formulas:
α + δ = 180°
β + γ = 180°
a + g2 = c + g1
g1 = √ d² - h²
g2 = √ b² - h²
α = arccos( (g1²+d²-h²) / ( 2*g1*d ) )
γ = arccos( (g2²+b²-h²) / ( 2*g2*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).
The obtuse trapezoid has an acute and an obtuse angle at each base, with the two acutes and the two obtuse angles opposite each other. An obtuse trapezoid is more likely to be perceived as oblique or tilted. The parallelogram is always an obtuse trapezoid, with not just two, but all four opposite sides of the parallelogram being parallel to each other. If it is not a parallelogram, then the obtuse trapezoid has no symmetries. The formulas for calculating the obtuse trapezoid are almost the same as for the normal or acute trapezoid, only the relationship between the two parallel sides a and c and the two overlaps g1 and g2 is different. The two overlaps are not on one of the two parallel sides as with the normal trapezoid, but one overlap on each of these two sides, which are diagonally opposite each other. This results in other possible angles.