Two opposite sides of a parallelogram each have a length of #6 #. If one corner of the parallelogram has an angle of #(3 pi)/4 # and the parallelogram's area is #27 #, how long are the other two sides?

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Answer 1 · 2017-12-10T13:04:18

The other two sides are 6.3649 long each

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

#sin A = h / AD#
Given #AD = 6, sin A = sin (pi/4) = 0.707#

#h = AD * sin A = 6 * (0.707 )= 4.242#

Area of parallelogram = AB * h = 27
#:. AB = 27 / 4.242 = 26.3649#

The other two sides are #6.3649 # long each