Two rhombuses have sides with lengths of #2 #. If one rhombus has a corner with an angle of #pi/6 # 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 · 2016-09-17T04:39:04

#2sqrt2-2 =0.8284#

Area of rhombus 1 (corner angle #= 30^@#)

#A_1= 2xx 2sin30=2xx1=2#

Area of rhombus 2 (corner angle #=45^@)#

#A_2=2xx2sin45=2xxsqrt2/2=2sqrt2#

difference of area #=A_2-A_1=2sqrt2-2=0.8284#

Or solution 2:

difference of area #=2(2sin45-2sin30)=0.8284#