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

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Answer 1 · 2017-07-23T13:21:51

See explanation.

The area of a parallelogram can be calculated as:

#A=1/2xxaxxbxxsinalpha#

where #a# and #b# are the sides and #alpha# is the angle between them.

#A=1/2xxaxxbxxsinalpha#

#2A=axxbxxsinalpha#

#b=(2A)/(axxsinalpha)#

Here we have:

#b=(2xx32)/(3sin(pi/4))#

#b=64/(3*sqrt(2)/2)#

#b=64xx2/(3sqrt(2))#

#b=128/(3sqrt(2))#

#b=(128sqrt(2))/6=(64sqrt(2))/3#