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 #36 #, how long are the other two sides?

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Answer 1 · 2017-12-10T12:55:05

The other two sides are 12.7298 long each

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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) = 0.707#

#h = AD * sin A = 4 * (0.707 )= 2.828#

Area of parallelogram = AB * h = 36
#:. AB = 36 / 2.828 = 12.7298#

The other two sides are #12.7298 # long each