Two rhombuses have sides with lengths of #8 #. If one rhombus has a corner with an angle of #(5pi)/12 # and the other has a corner with an angle of #(3pi)/8 #, what is the difference between the areas of the rhombuses?

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Answer 1 · 2016-06-04T09:04:12

One rhombus has larger area than the other by #2.688# units.

Area of rhombus of side #a# and included angle #theta# is given by

#a^2xxsintheta#

Hence area of one rhombus of side #8# and angle #(5pi)/12# is #8^2sin((5pi)/12)=64xx0.9659=61.8176#

and area of other rhombus of side #8# and angle #(3pi)/8# is #8^2sin((3pi)/8)=64xx0.9239=59.1296#

Hence one rhombus has larger area than the other by #61.8176-59.1296=2.688# units.