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 #pi/8 #, what is the difference between the areas of the rhombuses?

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Answer 1 · 2018-06-28T14:44:59

Difference in area between the 2 Rhombus

#color(indigo)(A_d = 1.53 - 1.04 = 0.49# sq units

Area of Rhombus #A = s^2 sin theta#

Given #s = 2, theta_1 = pi/12, theta_2 = pi/8#

#A_1 = s^2 sin theta_1 = 2^2 sin (pi/12) ~~ 1.04#

#A_2 = s^2 sin theta_2 = 2^2 sin (pi/8) ~~ 1.53#

Difference in area between the 2 Rhombus

#A_d = 1.53 - 1.04 = 0.49# sq units