Question

Two rhombuses have sides with lengths of `5`. If one rhombus has a corner with an angle of `pi/12` and the other has a corner with an angle of `(11pi)/12`, what is the difference between the areas of the rhombuses?

Answer 1

Difference in areas is `color(red)(0)`

Explanation:

Area of rhombus `= (1/2) * d_1 * d_2 or a * h`
Where `d_1 , d_2` are the diagonals, a is the side and h is the altitude.

In this case we will use the formula Area = a * h.

Rhombus 1
`h = a sin theta = 5 * sin (pi/12) = 1.2941`
Area = a * h = 5 * 1.2941 = 6.4705#

Rhombus 2
`h a sin theta = 5 * sin (11pi)/12 = 1.2941`
Area = a * h = 5 * 1.2941 = 6.4705#

Both the rhombus will have same area as `sin (pi/12) = sin ((11pi)/12)`
Hence the difference in areas is 0