Question

Two rhombuses have sides with lengths of `3`. If one rhombus has a corner with an angle of `pi/12` and the other has a corner with an angle of `(7pi)/8`, what is the difference between the areas of the rhombuses?

Answer 1

We know the area (A )of a rhombus is
`A=a^2sintheta`,where a is the length of the side and `theta` is the angle between two sides,
For 1st Rhombus `theta =pi/12,a=3`
So Area `A_1=3^2sin(pi/12)=2.33squnit`

For 2nd Rhombus `theta =7pi/8,a=3`
So Area `A_2=3^2sin(7xxpi/12)=8.69squnit`

So difference between the area `Delta A=A_2_A_1=8.69-2.33=6.36squnit`