Question

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?

Answer 1

`=3.43`

Explanation:

Area of rhombus with angle `theta=a^2 sintheta` where `a` is the side.
So Area `A1`of 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 `A2`of 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`