Parallelogram Perimeter Calculator

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)

  This is very similar to what you will find in our perimeter of a rectangle calculator or perimeter of a square calculator.

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 from the 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 the 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).

To use the parallelogram perimeter calculator, follow the steps:

1. Determine which part of the calculator is the one you need. Assume it's the 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.