TrapezoidVEXQOMIRA / GEOMETRY 10
Trapezoid Vexqomira

Formulas, without the guesswork.

Choose a relationship from the measurements you know. The variable names below belong to each calculator; a letter can have a different role in another method. π is evaluated using the browser’s full numerical constant, rather than replacing it with 3.14.

Two bases and height

A = (a+b)h/2

Inputs: Base a (length units); Base b (length units); Height h (length units).

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Two bases and two legs

Δ = |a−b|; x = (c²−d²+Δ²)/(2Δ); h = √(c²−x²)

Inputs: Base a (length units); Base b (length units); Leg c (length units); Leg d (length units).

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Isosceles trapezoid

h = √[c²−(a−b)²/4]

Inputs: Base a (length units); Base b (length units); Equal leg c (length units).

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Area to height

h = 2A/(b+c)

Inputs: Area A (square units); Base b (length units); Other base c (length units).

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Reading the notation

√ means a square root, ∛ means a cube root, and a superscript ² or ³ means a square or cube. Sine, cosine and tangent use angles converted from entered degrees. Where an inverse trigonometric function is used, its displayed angle is converted back to degrees. The ellipse perimeter is approximate; other formula labels describe the ideal mathematical model.

Equal bases with arbitrary legs do not uniquely determine a height. The four-side tool rejects that ambiguous case.

Reference reading: Trapezoid at Wolfram MathWorld.