Two rhombuses have sides with lengths of #7 #. If one rhombus has a corner with an angle of #pi/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 · 2018-05-27T15:49:28

Difference in area of rhombus = 21.97# sq units

Area of rhombus #A_r = a^2 sin theta# where a is the side and theta the included angle.

#a = 7, theta_1 = pi/12, theta_2 = pi/4#

#A_(r1) = 7^2 * sin (pi/12) = 12.68# sq units

#A_(r2) = 7^2 * sin (pi/4) = 34.65# sq units

Difference in area = 34.65 - 12.68 = 21.97# sq units