Two opposite sides of a parallelogram each have a length of #4 #. If one corner of the parallelogram has an angle of #(2 pi)/3 # and the parallelogram's area is #28 #, how long are the other two sides?

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Answer 1 · 2017-11-23T22:27:22

#(14sqrt(3))/3~~8.08# ( 2 .d.p.)

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Opposite angles are equal so A=C

The sum of all the angles is #2pi#

So Angle D is:

#D=(2pi-(4pi)/3)/2=pi/3#

#h=4sin(pi/3)=2sqrt(3)#

#Area of a parallelogram is:

#A=bh##:.#Area = base x height.

#28= b(2sqrt(3))=>b=28/(2sqrt(3))=(14sqrt(3))/3#

So other two sides are:

#(14sqrt(3))/3~~8.08# ( 2 .d.p.)