Two rhombuses have sides with lengths of #12 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #pi/8 #, what is the difference between the areas of the rhombuses?

Question

1063 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-08T12:59:00

the difference is:

#144(sin(pi/8)-sin(pi/12))~=17.84#

In the first rhombus, whose angle is #pi/12#, the area is:

#cancel2*12*12*sin(pi/8)*1/cancel2=144sin(pi/8)#

In the second one, whose angle is #pi/12#, the area is:

#cancel2*12*12*sin(pi/12)*1/cancel2=144sin(pi/12)#

Then the difference is:

#144(sin(pi/8)-sin(pi/12))~=17.84#