Two rhombuses have sides with lengths of #15 #. If one rhombus has a corner with an angle of #(7pi)/8 # and the other has a corner with an angle of #(5pi)/6 #, what is the difference between the areas of the rhombuses?

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Answer 1 · 2016-08-19T13:46:59

#=26.4#

Area of the rhombus with angle #theta=(7pi)/8# and Side #a=15# is
#=a^2 sin theta#

#=15^2 sin((7pi)/8)#

#=225(0.383)#

#=86.1#

Area of the rhombus with angle #theta=(5pi)/6# and Side #a=15# is

#=a^2 sin theta#

#=15^2 sin((5pi)/6)#

#=225(0.5)#

#=112.5#

So difference in Area#=112.5-86.1=26.4#