Two rhombuses have sides with lengths of #5 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #(7pi)/12 #, what is the difference between the areas of the rhombuses?

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Answer 1 · 2016-08-24T11:33:39

#=17.68#

Area of the rhombus with angle #theta=(pi)/12# and Side #a=5# is
#=a^2 sin theta#

#=5^2 sin((pi)/12)#

#=25(0.2588)#

#=6.47#

Area of the rhombus with angle #theta=(7pi)/12# and Side #a=5# is

#=5^2 sin theta#

#=5^2 sin((7pi)/12)#

#=25(0.966)#

#=24.15#

So difference in Area#=24.15-6.47=17.68#