Two rhombuses have sides with lengths of #7 #. If one rhombus has a corner with an angle of #pi/4 # and the other has a corner with an angle of #(3pi)/4 #, what is the difference between the areas of the rhombuses?

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Answer 1 · 2018-02-28T12:03:10

Both rhombuses are identical and hence no difference in areas.

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Given #a = 7, theta_1 = pi/4, theta_2 = ((3pi)/4)#

Area of Rhombus #A_r = a^2 sin theta#

We know, sin theta = sin pi - theta)#

#:. sin (3pi)/4 = sin (pi - (3pi)/4) = sin (pi/4)#

In both the rhombuses, theta is #(pi/4)#. Hence, their areas are the same

#A_r = 7^2 sin (pi/4) = 49 / sqrt2 = 34.6482#