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/3 , what is the difference between the areas of the rhombuses?

1 Answer
Aug 5, 2016

=3.43

Explanation:

Area of rhombus with angle theta=a^2 sintheta where a is the side.
So Area A1of rhombus with side-length 2
and angle pi/12 can be written as
A1=(2^2) sin(pi/12)
or
A1=4sin(pi/12)
or
A1=1.03
And Area A2of rhombus with side-length 2
and angle pi/3 can be written as
A2=(2^2) sin(pi/3)
or
A2=4 sin(pi/3)
or
A2=3.46
The difference
=A2-A1
=3.46-1.03
=3.43