Question

Two rhombuses have sides with lengths of `8`. If one rhombus has a corner with an angle of `pi/4` and the other has a corner with an angle of `(3pi)/8`, what is the difference between the areas of the rhombuses?

Answer 1

`=13.88`

Explanation:

Area of the rhombus with angle `theta=(pi)/4` and Side `a=8` is
`=a^2 sin theta`
`=8^2 sin((pi)/4)`
`=64(0.707)`
`=45.25`
Area of the rhombus with angle `theta=(3pi)/8` and Side `a=8` is
`=a^2 sin theta`
`=8^2 sin((3pi)/8)`
`=64(0.924)`
`=59.13`
So difference in Area`=59.13-45.25=13.88`