Two rhombuses have sides with lengths of #9 #. If one rhombus has a corner with an angle of #(7pi)/12 # and the other has a corner with an angle of #(pi)/4 #, what is the difference between the areas of the rhombuses?

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Answer 1 · 2018-07-06T00:03:41

#10.482\ \text{unit}^2#

The area (#A_1#) of rhombus with each side #a=9# & corner angle #\theta={7\pi}/12# is given as follows

#A_1=1/2(a)(a)\sin\theta#

#=1/2(9)(9)\sin({7\pi}/12)#

#=81/2\sin({7\pi}/12)#

The area (#A_2#) of rhombus with each side #a=9# & corner angle #\theta={\pi}/4# is given as follows

#A_2=1/2(a)(a)\sin\theta#

#=1/2(9)(9)\sin({\pi}/4)#

#=81/2sin({\pi}/4)#

Now, the difference of areas of rhombus

#A_1-A_2#

#=81/2\sin({7\pi}/12)-81/2\sin({\pi}/4)#

#=10.482\ \text{unit}^2#