Question

How do you find the perimeter of a parallelogram?

Answer 1

`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)`