Question

Two rhombuses have sides with lengths of `1`. If one rhombus has a corner with an angle of `(7pi)/12` and the other has a corner with an angle of `(pi)/4`, what is the difference between the areas of the rhombuses?

Answer 1

`=0.26`

Explanation:

Area of the rhombus with angle `theta=(7pi)/12` and Side `a=1` is
`=a^2 sin theta`
`=1^2 sin((7pi)/12)`
`=1(0.966)`
`=0.966`
Area of the rhombus with angle `theta=pi/4` and Side `a=1` is
`=a^2 sin theta`
`=1^2 sin((pi)/4)`
`=1(0.707)`
`=0.707`
So difference in Area`=0.966-0.707=0.26`