Two rhombuses have sides with lengths of #6 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #pi/6 #, what is the difference between the areas of the rhombuses?

1 Answer
Jim G.
Apr 12, 2016

≈ 8.68 square units

Explanation:

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

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

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

hence area of 1st rhombus #= 6^2 sin(pi/12) ≈ 9.32#

and area of 2nd rhombus #= 6^2 sin(pi/6) = 18 #

Difference in area = 18 - 9.32 = 8.68 square units

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