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
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
