Two rhombuses have sides with lengths of #4 #. If one rhombus has a corner with an angle of #(11pi)/12 # and the other has a corner with an angle of #(pi)/4 #, what is the difference between the areas of the rhombuses?

Question

1291 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-09-15T05:05:59

#11.314-4.141 =7.173#

enter image source here

Area of rhombus #= bxxh#

Rhombus 1 :

#h=4sin15= 1.0353#

Area 1 (A1) #= 4xx1.0353 = 4.141#

Rhombus 2:

#h=4sin45=2.8284#

Area 2 (A2) #=4xx2.8284=11.314#

Difference between A1 and A2 :

#=> 11.314-4.141 = 7.173#

Or solution 2 :

difference of areas :

#4(4sin45-4sin15)=7.173#