Two rhombuses have sides with lengths of #5 #. If one rhombus has a corner with an angle of #(pi)/6 # 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 · 2018-02-28T11:34:38

#d = =color(purple)( 5.1777# sq units

Area of Rhombus
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Given #a = 5, theta_1 = pi/6, theta_2 = (3pi)/4#

Area #A_1 = a^2 sin theta_1 = 5^2 sin (pi/6) = 12.5# sq units

Area #A_2 = a^2 sin theta_2 = 5^2 sin ((3pi)/4) = 17.6777# sq units

Difference in areas between the two rhombuses is

#d = 17.6777 - 12.5 =color(purple)( 5.1777# sq units