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

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Answer 1 · 2016-03-21T15:24:26

#=15sqrt2/2#

Area of a parallelogram # A =a*b*sintheta#

Here #A=45;a = 6;b=?;theta =3pi/4 #

So
#45=6*b*sin(3pi/4)#
#45=6*b*sin(pi-pi/4)#
#45=6*b*sin(pi/4)#
#45=6*b*1/sqrt2#
#b=(45sqrt2)/6=15sqrt2/2#