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How to Find the Area of a Parallelogram if You Know the Height and Perimeter

The formula for finding the area of a parallelogram is base length multiplied by height length. The perimeter of a parallelogram is determined by finding the sum of all of the parallelogram's side length measurements. Just knowing the height and perimeter of a parallelogram is not enough, on its own, to determine the area the parallelogram. You need more information. For example, if you only know the total perimeter measurement of the parallelogram and not the individual base length, the parallelogram's area can be calculated if the base angle is known.

Things You'll Need

  • Scientific calculator
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Instructions

    • 1

      Enter the base angle amount in a scientific calculator. Press the "sin" button to calculate the sin.

      Example: For a parallelogram with a perimeter of 28.194 cm, a height of 4 cm, and a base angle amount of 41 degrees, the sin of 41 degrees is approximately 0.656.

    • 2

      Divide the height amount by the result in Step 1. This (quotient) result is the length of one side of the parallelogram.

      Example: 4 / 0.656 = 6.097, approximately.

    • 3

      Multiply the result from Step 2 by 2. This (product) result is the total length of the two (left and right) sides of the parallelogram.

      Example: 6.097 * 2 = 12.194.

    • 4

      Subtract the result from Step 3 from the perimeter. This (difference) result is the total length of the top and bottom sides of the parallelogram.

      Example: 28.194 - 12.194 = 16.

    • 5

      Divide the result from Step 4 by 2. This (quotient) result is the base length of the parallelogram.

      Example: 16 / 2 = 8.

    • 6

      Multiply the base length of the parallelogram by the height. The result is the area of the parallelogram.

      Example: 8 * 4 = 32.

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