Two opposite sides of a parallelogram have lengths of #3 #. If one corner of the parallelogram has an angle of #pi/4 # and the parallelogram's area is #36 #, how long are the other two sides?

1 Answer
sankarankalyanam
Feb 28, 2018

Other two parallel sides are #color(green)(12sqrt2# long each.

Explanation:

![http://www.mathatube.com/http://geometry-area-of-a-parallelogram.html](https://useruploads.socratic.org/rsNdIAEQFyL06MZeAQwg_465A1730-B48E-4F8D-B8A6-06F1C749EA22.jpeg)

Area of parallelogram #A_p = b h = b a sin theta# as #h = a sin theta #

Given : #b = 3, A_p = 36, theta = pi/4#

To find a.

# a = A_p / (b sin theta) = cancel(36)^color(brown)(12) / (cancel(3 ) sin (pi /4) )= 12 / (1/sqrt2) = 12 sqrt2#

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