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How to Find the Perimeter of a Parallelogram With Variables

A parallelogram is a quadrilateral, a four-sided geometric construction. The opposite sides of a parallelogram are always equal in length and are always parallel to one another. A rectangle is a parallelogram, but not all parallelograms are rectangles. The base of a parallelogram refers to the length of the side on the bottom (identical to the side on the top). The other side is simply termed the side. The height is the distance from the top side to the base. Given some information about a parallelogram, you can deduce other facts, including the perimeter.

Things You'll Need

Scientific calculator

Instructions

- 1
  Assign these variables to describe the parallelogram: b = length of the base, a= length of a side, m = perimeter, h=height, p = length of the short diagonal, q = length of the long diagonal, A= acute internal angle, B= obtuse internal angle and s = area.
- 2
  Use this formula for the perimeter: m = 2(a+b). If you already know the length of both the base and side, determining the perimeter is as simple as this: Add them together and multiply by two.
- 3
  Use the formula p^2 + q^2 = 2(a^2 + b^2) to find the length of either the side or the base given the other one, as well as the length of both diagonals.
- 4
  Use the formula s = b x h, which relates the volume of the parallelogram to its height and base. If you are given the volume, the height and the length of the side, you can divide volume by height to get the length of the base, then calculate the perimeter.
- 5
  Use the formula S = a x b x sin A, if you are given the area, length of either the base or the side, and one of the angles. Remember that there are two equal acute angles in a (non-rectangular) parallelogram and two equal obtuse angles. The acute and obtuse angle will sum to 180 degrees, so if you know one angle, you know them all. The sine of an angle A will be equal to the sine of (180-A), so it doesn't matter whether you use the acute or obtuse angle. Divide area by the sine of the angle, then divide by the length of either a or b. The result will be the missing value (a or b). Knowing both a and b, you can quickly determine the perimeter.

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