Two rhombuses have sides with lengths of #5 #. 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 · 2017-07-06T11:15:13

Area of rhombuses are #25 and 23.1# sq.unit

Area of rhombus with known side #S# and corner angle #theta# is

#A_r= s^2 sin theta#

Area of rhombus (1) # S=5 , theta= pi/2=90^0 :. A_(r1) = 5^2*sin90 =25 # sq.unit

Area of rhombus (2) # S=5 , theta= (3pi)/8=67.5^0 :. A_(r1) = 5^2*sin67.5 ~~23.1 # sq.unit

Area of rhombuses are #25 and 23.1# sq.unit [Ans]