Two opposite sides of a parallelogram each have a length of #4 #. If one corner of the parallelogram has an angle of #(3 pi)/4 # and the parallelogram's area is #32 #, how long are the other two sides?

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Answer 1 · 2017-12-04T09:57:02

Length of the other two sides are #8 sqrt2 = 11.3137# long.

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#/_A+ /_B= pi#
#/_B= (3pi)/4#
#:./_A= pi - (3pi)/4 = pi/4#

#sin A = h / AD#
Given #AD = 4, sin A = sin (pi/4) = 1/sqrt2#

#h = AD * sin A = 4 / sqrt 2#

Area of parallelogram = AB * h = 32
#:. AB = 32 / h = 32 / (4/sqrt2)#
#AB = 8 sqrt 2 #

The other two sides are #8 sqrt2 # long