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Perimeter
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# Parallelogram Perimeter Calculator

By Hanna Pamuła, PhD candidate

If you ever wondered how to find the perimeter of a parallelogram, this parallelogram perimeter calculator can help you in no time. Not only we implemented the easiest well-known equation but also two other parallelogram perimeter formulas. Why not give it a go? Check out also twin brother of that calculator - parallelogram area calculator - to get to know this shape better.

## Parallelogram perimeter formula

The most well known formula for parallelogram perimeter comes from perimeter definition: it's simply the sum of the lengths of sides: • `perimeter = a + b + a + b = 2 * (a + b)`

But what if we don't have the length of the two sides? • Perimeter given one side and diagonals

If you know the diagonals and two sides, you can use the formula:

`perimeter = 2 * a² + √(2 * e² + 2 * f²- 4 * a²)`

Where does it come from? It's transformed parallelogram law which states that the sum of the squares of the lengths of the four sides of a parallelogram equals the sum of the squares of the lengths of the two diagonals:

`2 * a² + 2 * b² = e² + f²` • Perimeter given base, height and any parallelogram angle

It's the formula using trigonometric sine function:

`perimeter = 2 * (a + (h/sin(angle)))`

The adjacent angles in the parallelogram are supplementary, so you can choose whichever angle you want because sin(angle) equals sin(180° - angle).

## How to find the perimeter of a parallelogram using this calculator?

To use the parallelogram perimeter calculator follow the steps:

1. Determine which part of the calculator is the one you need. Assume it's second part.
2. Type the values - in this case, side (a) and two diagonals (e, f): 15 in, 18 in and 24 in, respectively. If you enter the values which can't form the parallelogram, the calculator will tell you about it. (Think for a while, why is it not always possible to create a parallelogram? Take a=1, e=15, f=4, is it possible to create the triangle from a, e/2 and f/2?)
3. Parallelogram perimeter calculator displays the value. It's 60 in².

## What next?

If you are happy with the results from parallelogram perimeter calculator, maybe you want to check our other geometry calculators?

Hanna Pamuła, PhD candidate