Question

Two rhombuses have sides with lengths of `8`. If one rhombus has a corner with an angle of `(7pi)/12` and the other has a corner with an angle of `(pi)/6`, what is the difference between the areas of the rhombuses?

Answer 1

Difference in areas between two rhombuses is 21.8192

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 = 8 * sin ((pi)/6) = 4`
Area = a * h = 8 * 4 = 32#

Rhombus 2
`h = a sin theta = 8 * sin ((7pi)/12) = 7.7274`
Area = a * h = 8 * 7.7274 = 61.8192#

Hence the difference in areas is `61.8192 - 32 = 21.8192`