Two opposite sides of a parallelogram each have a length of #12 #. If one corner of the parallelogram has an angle of #(3pi)/8 # and the parallelogram's area is #24 #, how long are the other two sides?

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Answer 1 · 2016-04-29T08:03:59

Other two sides are #2.165# units long.

Area of a parallelogram whose one pair of sides are #a#, other pair of sides are#b# and included angle is #theta# is given by

#axxbxxsintheta#

As area of parallelogram is #24#, one pair of sides have length #12# and included angle is #(3pi)/8#, we have

#12xxbxxsin((3pi)/8)=24# or

#12xxbxx0.9239=24# and hence

#b=24/(12xx0.9239)=(2cancel24)/(1cancel12xx0.9239)=2/0.9239=2.165#