Isosceles Trapezoid, calculator and formula

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.

Trapezoid calculator

Input

Side d

Side a

Side c

Decimal places

Results

Side a

Side b / d

Side c

Diagonal e

Height h

Mean width m

Area A

Perimeter P

Angle α / β

Angle γ / δ

Excess x / y

Side \(a\)

\(\displaystyle a = \frac{A · 2} {h}-c\)

\(a = m · 2 -c\)

Side \(b\)

\(\displaystyle b = \frac{h}{ sin(β)}\)

\(\displaystyle b = \frac{h}{sin(γ)}\)

Side \(c\)

\(\displaystyle c = \frac{ A · 2}{ h} - a\)

\(\displaystyle c = m · 2 - a\)

Side \(d\)

\(\displaystyle d = h / sin(α)\)

\(d = h / sin(δ)\)

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 \(h\)

\(\displaystyle h = \frac{2 · A} {a + c}\)

\(h = b · sin(β)\)

Area \(A\)

\(\displaystyle A = \frac{(a + c) · h} { 2 }\)

\(A = m · h\)

Perimeter \(P\)

\(\displaystyle P = a + b + c + d\)

Mean Width \(m\)

\(\displaystyle m = \frac{a + c} { 2}\)

\(\displaystyle m = A / h\)

Angle Alpha \(α\)

\(\displaystyle α = asin\left(\frac{h}{d}\right)\)

\(\displaystyle α = 180 - δ\)

Angle Beta \(β\)

\(\displaystyle β = asin\left(\frac{h}{b}\right)\)

\(\displaystyle β = 180 - γ\)

Angle Gamma \(γ\)

\(\displaystyle γ = 180 - β\)

Angle Delta \(δ\)

\(\displaystyle δ = 180 - α\)

Excess \(x\)

\(\displaystyle x = \sqrt{d^2-h^2}\)

Excess \(y\)

\(\displaystyle y = \sqrt{b^2-h^2}\)

Isosceles Trapezoid

Calculate parameters of a isosceles trapezoid

Formulas for a isosceles trapezoid