Two opposite sides of a parallelogram each have a length of #10 #. If one corner of the parallelogram has an angle of #(3 pi)/4 # and the parallelogram's area is #80 #, how long are the other two sides?

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Answer 1 · 2016-10-26T17:12:14

The other two sides are each #8sqrt(2)# long.

The area of a parallelogram is

#A = bh#

Given:

The Area, #A = 80#
The base, #b= 10#

Compute h:

#h = 80/10 = 8#

The given angle is greater than #pi/2# so we need to compute the other angle:

#theta = pi - (3pi)/4 = pi/4#

The length of the other side, #s = h/sin(theta) = 8/sin(pi/4) = 8sqrt(2) #