Two opposite sides of a parallelogram each have a length of #12 #. If one corner of the parallelogram has an angle of #(5 pi)/12 # and the parallelogram's area is #132 #, how long are the other two sides?

Question

1024 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-12-10T12:34:22

The two other sides are 10.0816 long each

enter image source here
#/_A+ /_B= pi#
#/_B= (7pi)/8#
#:./_A= pi - (5pi)/12 = (7pi)/12#

#sin A = h / AD#
Given #AD = 12, sin A = 12 * sin ((7pi)/12) = 11.5911#

#h = AD * sin A = 12 * (11.5911 )= 13.0932#

Area of parallelogram = AB * h = 132
#:. AB = 132 / 13.0932 = 10.0816#

The other two sides are #10.0816 # long each