Two rhombuses have sides with lengths of 2 2. If one rhombus has a corner with an angle of pi/12 π12 and the other has a corner with an angle of pi/3 π3, what is the difference between the areas of the rhombuses?

1 Answer
Aug 5, 2016

=3.43=3.43

Explanation:

Area of rhombus with angle theta=a^2 sinthetaθ=a2sinθ where aa is the side.
So Area A1A1of rhombus with side-length 22
and angle pi/12π12 can be written as
A1=(2^2) sin(pi/12)A1=(22)sin(π12)
or
A1=4sin(pi/12)A1=4sin(π12)
or
A1=1.03A1=1.03
And Area A2A2of rhombus with side-length 22
and angle pi/3π3 can be written as
A2=(2^2) sin(pi/3)A2=(22)sin(π3)
or
A2=4 sin(pi/3)A2=4sin(π3)
or
A2=3.46A2=3.46
The difference
=A2-A1=A2A1
=3.46-1.03=3.461.03
=3.43=3.43