Two rhombuses have sides with lengths of #2 #. If one rhombus has a corner with an angle of #(3pi)/8 # 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 · 2018-01-14T07:35:44

Difference in area between the two rhombuses

#A_d = color(red)(0.0457)#

Area of Rhombus #A_r = a * a sin theta# where ‘a’ is the side of the rhombus and ‘theta’ measure of one corner angle.

Rhombus 1 :

#A_(r1) = 2 * 2 sin ((3pi)/8) = color(blue)(0.0822)#

#A_(r2) = 2 * 2 sin ((7pi)/12) = color (blue)(0.1279)#

Difference in area between the two rhombuses

#A_d = A_(r2) - A_(r1) = 0.1279 - 0.0822 = color(red)(0.0457)#