Isosceles Trapezoid
Calculator and formulas for calculating a isosceles trapezoid
To calculate the isosceles trapezoid, enter either the sides a and c, as well as the height or the sides a and d and the angle alpha. Then click on the 'Calculate' button.
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Formulas for the trapezium
Side length (a)
\(\displaystyle a = \frac{A · 2} {h}-c\) \(\displaystyle \ \ \ = m · 2 -c\)
Side length (b)
\(\displaystyle b = \frac{h}{ sin(β)}\) \(\displaystyle \ \ \ = \frac{h}{sin(γ)}\)
Side length (c)
\(\displaystyle c = \frac{ A · 2}{ h} - a\) \(\displaystyle \ \ \ = m · 2 - a\)
Side length (d)
\(\displaystyle d = \frac{h}{sin(α)}\) \(\displaystyle \ \ \ = \frac{h}{sin(δ)}\)
Diagonal (e)
\(\displaystyle e = \sqrt{a^2 + b^2 - 2 · a · b · cos(β)}\)
Diagonal (f)
\(\displaystyle f = \sqrt{a^2 + d^2 - 2 · a · d · cos(α)}\)
Height (h)
\(\displaystyle h = \frac{2 · A} {a + c}\) \(\displaystyle \ \ \ = b · sin(β)\)
Area (A)
\(\displaystyle A = \frac{(a + c) · h} { 2 }\) \(\displaystyle \ \ \ = m · h\)
Perimeter (P)
\(\displaystyle P = a + b + c + d\)
Medium width (m)
\(\displaystyle m = \frac{a + c} { 2}\) \(\displaystyle \ \ \ = \frac{A}{h}\)
Angle Alpha (α)
\(\displaystyle α = asin\left(\frac{h}{d}\right)\) \(\displaystyle \ \ \ = 180 - δ\)
Angle Beta (β)
\(\displaystyle β = asin\left(\frac{h}{b}\right)\) \(\displaystyle \ \ \ = 180 - γ\)
Angle Gamma (γ)
\(\displaystyle γ = 180 - β\)
Angle Delta (δ)
\(\displaystyle δ = 180 - α\)
Excess (x)
\(\displaystyle x = \sqrt{d^2-h^2}\)
Excess (y)
\(\displaystyle y = \sqrt{b^2-h^2}\)
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