Two opposite sides of a parallelogram each have a length of #8 #. If one corner of the parallelogram has an angle of #(3pi)/8 # and the parallelogram's area is #48 #, how long are the other two sides?

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Answer 1 · 2016-10-10T18:14:58

Each of the other sides are approximately 6.49 units long.

The area, A of a parallelogram is the product of its base, b, and is height, h:

#A = bh#

We are given, #A = 48#, and #b = 8#. We can use this to solve for the height:

#48 = 8h#

#h = 6#

The length of the other sides, s, can be found using the equation:

#h = (s)sin(theta)#

#s = 6/sin((3pi)/8)#

#s ~~ 6.49 #