Two rhombuses have sides with lengths of #2 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #pi/4 #, what is the difference between the areas of the rhombuses?
1 Answer
Apr 4, 2016
≈ 1.793 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 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 of rhombus =
#2xx1/2a^2sintheta = a^2sintheta # hence area of 1st rhombus
#= 2^2sin(pi/12) ≈ 1.035# and area of 2nd rhombus =
#2^2sin(pi/4) ≈ 2.828 # Difference in area = 2.828 - 1.035 = 1.793 square units
