Question

Two rhombuses have sides with lengths of `3`. If one rhombus has a corner with an angle of `(7pi)/12` and the other has a corner with an angle of `(pi)/6`, what is the difference between the areas of the rhombuses?

Answer 1

`=4.19`

Explanation:

Area of rhombus with angle `theta=a^2 sintheta` where `a` is the side.
So Area `A1`of rhombus with side-length `3`
and angle `7pi/12` can be written as
`A1=(3^2) sin(7pi/12)`
or
`A1=9sin(7pi/12)`
or
`A1=8.69`
And Area `A2`of rhombus with side-length `3`
and angle `pi/6` can be written as
`A2=(3^2) sin(pi/6)`
or
`A2=9 sin(pi/6)`
or
`A2=4.5`
The difference
`=A2-A1`
`=8.69-4.5`
`=4.19`