Question

Two rhombuses have sides with lengths of `6`. If one rhombus has a corner with an angle of `pi/12` and the other has a corner with an angle of `(3pi)/4`, what is the difference between the areas of the rhombuses?

Answer 1

`=16.14`

Explanation:

Area of the rhombus with angle `theta=(pi)/12` and Side `a=6` is
`=a^2 sin theta`
`=6^2 sin((pi)/12)`
`=36(0.2588)`
`=9.32`
Area of the rhombus with angle `theta=(3pi)/4` and Side `a=6` is
`=a^2 sin theta`
`=6^2 sin((3pi)/4)`
`=36(0.707)`
`=25.46`
So difference in Area`=25.46-9.32=16.14`