Two rhombuses have sides with lengths of #3 #. If one rhombus has a corner with an angle of #pi/2 # 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 · 2018-05-22T04:31:09

Difference between the areas of 2 rhombus is

#A_d = A_1 - A_2 = 9 - 8.31 = 0.69# sq units

Area of rhombus #A = a^2 sin theta#

Given : #a_1 = a_2 = 3, theta_1 = pi/2, theta_2 = (3pi)/8#

Area of Rhombus #A_1 = (a_1)^2 sin theta_1#

#A_1 = 3^2 sin (pi/2) = 9# sq units, it’s a square since #theta = 90^@ = (pi/2)^c#

Area of Rhombus #A_2 = (a_2)^2 sin theta_2#

#A_2 = 3^2 sin ((3pi)/8) = 8.31# sq units

Difference between the areas of 2 rhombus is

#A_d = A_1 - A_2 = 9 - 8.31 = 0.69# sq units