Online calculator and formulas for unsymmetrical trapezoids
To calculate the trapezoid, either the sides a and c as well as the height and the projection x are entered; alternatively, an angle and 3 side lengths can be specified.
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Side length \(a \) |
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\(\displaystyle a = \frac{A · 2} {h}-c\) | \(a = m · 2 -c\) |
Side length \(b \) |
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\(\displaystyle b = \frac{h}{ sin(β)}\) | \(\displaystyle b = \frac{h}{sin(γ)}\) |
Side length \(c \) |
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\(\displaystyle c = \frac{ A · 2}{ h} - a\) | \(\displaystyle c = m · 2 - a\) |
Side length \(d \) |
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\(\displaystyle d = h / sin(α)\) | \(d = h / sin(δ)\) |
Diagonal \(e \) |
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\(\displaystyle e = \sqrt{a^2 + b^2 - 2 · a · b · cos(β)}\) | |
Diagonal \(f \) |
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\(\displaystyle f = \sqrt{a^2 + d^2 - 2 · a · d · cos(α)}\) | |
Height \(h\) |
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\(\displaystyle h = \frac{2 · A} {a + c}\) | \(h = b · sin(β)\) |
Width \(m \) |
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\(\displaystyle m = \frac{a + c} { 2}\) | \(\displaystyle m = A / h\) |
Area \(A \) |
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\(\displaystyle A = \frac{(a + c) · h} { 2 }\) | \(A = m · h\) |
Perimeter \(P \) |
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\(\displaystyle P = a + b + c+ d\) | |
Angle \(α \) |
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\(\displaystyle α = asin\left(\frac{h}{d}\right)\) | \(\displaystyle α = 180 - δ\) |
Angle \(β \) |
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\(\displaystyle β = asin\left(\frac{h}{b}\right)\) | \(\displaystyle β = 180 - γ\) |
Angle \(γ \) |
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\(\displaystyle γ = 180 - β\) | |
Angle \(δ \) |
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\(\displaystyle δ = 180 - α\) | |
Excess \(x \) |
\(\displaystyle x = \sqrt{d^2-h^2}\) | |
Excess \(y \) |
\(\displaystyle y = \sqrt{b^2-h^2}\) | |
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