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Short Edge of Parallelogram given Diagonals and Long Edge Calculator

Formula

The formula to calculate the Short Edge of Parallelogram given Diagonals and Long Edge is:

$e_{\text{Short}} = \sqrt{\frac{d_{\text{Long}}^2 + d_{\text{Short}}^2 - (2 \cdot e_{\text{Long}}^2)}{2}}$

Definition

The Short Edge of a Parallelogram is the length of the shortest pair of parallel edges in a Parallelogram. The Long Diagonal of a Parallelogram is the length of the line joining the pair of acute angle corners of a Parallelogram. The Short Diagonal of a Parallelogram is the length of the line joining the pair of obtuse angle corners of a Parallelogram. The Long Edge of a Parallelogram is the length of the longest pair of parallel sides in a Parallelogram.

Example Calculation

Let's assume the following values:

Long Diagonal of Parallelogram = 18 meters
Short Diagonal of Parallelogram = 9 meters
Long Edge of Parallelogram = 12 meters

Using the formula:

$e_{\text{Short}} = \sqrt{\frac{18^2 + 9^2 - (2 \cdot 12^2)}{2}} = 7.64852927038918$

The Short Edge of the Parallelogram is 7.64852927038918 meters.

Conversion Chart

Long Diagonal (meters)	Short Diagonal (meters)	Long Edge (meters)	Short Edge (meters)
16	9	12	4.949747468305833
16.5	9	12	5.711829829397931
17	9	12	6.403124237432849
17.5	9	12	7.044501401802686
18	9	12	7.648529270389178
18.5	9	12	8.223442101699263
19	9	12	8.774964387392123
19.5	9	12	9.307255234493143
20	9	12	9.823441352194250