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Two rhombuses have sides with lengths of #12 #. If one rhombus has a corner with an angle of #(5pi)/12 # and the other has a corner with an angle of #(7pi)/12 #, what is the difference between the areas of the rhombuses?

Answer 1

Avery Allen

no difference.Area's are equal.

A rhombus has 4 equal sides and is constructed from 2 congruent isosceles triangles.

The area of 1 triangle #= 1/2 a.a sintheta = 1/2 a^2sintheta #

where a is the length of side and # theta" the angle between them "#

Now the area of 2 congruent triangles (area of rhombus ) is.

area #= 2xx1/2a^2sintheta = a^2sintheta #

hence area of 1st rhombus #=12^2sin((5pi)/12) ≈ 139.093#

and area of 2nd rhombus#= 12^2sin((7pi)/12) ≈ 139.093 #

Area's of both are equal hence no difference.

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