Two rhombuses have sides with lengths of #12 #. If one rhombus has a corner with an angle of #pi/3 # and the other has a corner with an angle of #(5pi)/8 #, what is the difference between the areas of the rhombuses?

1 Answer
Jim G.
Mar 25, 2016

≈ 8.33 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.a sin theta = 1/2a^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 # = 2xx1/2a^2 sintheta = a^2 sintheta #

hence area of 1st rhombus #= 12^2sin(pi/3) ≈ 124.71#

and area of 2nd rhombus #= 12^2sin((5pi)/8) ≈ 133.04#

difference in area = 133.04 - 124.71 = 8.33 square units

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