How to Find a Side Length of a Parallelogram


The length of a parallelogram's side lets you calculate its perimeter. The length does not, however, directly tell you the shape's area. The area instead depends on the shape's height and width. If you do know the width and area, you can calculate the shape's height, and together this height, the side and part of the base form a triangle. You can then calculate the length of the parallelogram's side using trigonometry.

  • Divide the shape's area by its base's length to calculate its height. If, for instance, the parallelogram measures 10 square inches in area, and its base measures 4 inches in length, 10 / 4 = 2.5 inches. This is the shape's height.

  • Measure the acute angle between one side and at the shape's base. For this example, imagine an angle that measures 40 degrees.

  • Find the sine of the angle, using a calculator: sin (40) = 0.643.

  • Divide the height by this ratio: 2.5 / 0.643 = 3.89 inches. This is the length of the parallelogram's side.

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