Question

Two rhombuses have sides with lengths of `15`. If one rhombus has a corner with an angle of `pi/12` and the other has a corner with an angle of `(5pi)/6`, what is the difference between the areas of the rhombuses?

Answer 1

Difference in areas between the two rhombuses is 54.2655

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 = 15 * sin ((5pi)/6) = 7.5`
Area = a * h = 15 * 7.5 = 112.5#

Rhombus 2
`h = a sin theta = 15 * sin ((pi)/12) = 3.8823`
Area = a * h = 15 * 3.8823 = 58.2345

Hence the difference in areas is `112.5 - 58.2345 = 54.2655`