ParallelogramVEXQOMIRA / GEOMETRY 09
Parallelogram 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.

Base and perpendicular height

A = bh

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

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Sides and included angle

A = ab sin θ; P = 2(a+b)

Inputs: Side a (length units); Side b (length units); Included angle θ (degrees).

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Diagonals and crossing angle

A = pq sin θ/2

Inputs: Diagonal p (length units); Diagonal q (length units); Crossing angle θ (degrees).

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Area to perpendicular height

h = A/b

Inputs: Area A (square units); Base b (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.

A sloping side is not generally the height. Base and height alone do not determine perimeter.

Reference reading: Parallelogram at Wolfram MathWorld.