How do you find the perimeter of a parallelogram?

1 Answer
Jan 3, 2016

P=l+l+w+w
P=2l+2w
P=2(l+w)

Explanation:

Any parallelogram, such as the one pictured below, has opposite sides that are congruent. That means that bar(AB) and bar(CD) have the same length, and that bar(AD) and bar(BC) have the same length.

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Say you only knew the lengths of bar(AB) and bar(AD), and wanted to find the perimeter of the entire parallelogram. Even though they're not given to you, you know that bar(BC) is exactly as long as bar(AD) and bar(AB) is congruent to bar(CD).

Thus, the perimeter could be calculated through taking 2xxbar(AB)+2xxbar(AD), since there are essentially two of each side.

Through this, you can generalize to any parallelogram: the two widths will always be congruent, as will the two heights:

P=l+l+w+w
P=2l+2w
P=2(l+w)