Two rhombuses have sides with lengths of #2 #. If one rhombus has a corner with an angle of #pi/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 · 2016-10-20T16:51:33

#A_1 - A_2 ~~ 2.66#

#A = s^2 sin(theta)#

where #s# is the side and #theta# is one of its angles.

With both having equal sides, the difference is:

#A_1 - A_2 = s^2(sin(theta_1) - sin(theta_2))#

#A_1 - A_2 = 2^2(sin((3pi)/8) - sin(pi/12))#

#A_1 - A_2 ~~ 2.66#