Two rhombuses have sides with lengths of #12 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #pi/2 #, what is the difference between the areas of the rhombuses?

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Answer 1 · 2018-05-07T14:25:12

#color(purple)("Difference in Areas " = A_d = A_s - A_r = 144 - 37.27 = 106.73 "sq units"#

#Rhombus 1 : a = 12, theta = pi/12#

#"Area of Rhombus " A_(r) = a^2 sin theta = 12^2 sin (pi/12) = 37.27#

#Rhombus 2 : a = 12, theta = pi/2, " it's a square as "theta = pi/2#

#"Area of Square " A_(s) = a^2 = 12^2 = 144#

#color(purple)("Difference in Areas " = A_d = A_s - A_r = 144 - 37.27 = 106.73 "sq units"#