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)#