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
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
