Question

Two rhombuses have sides with lengths of `7`. If one rhombus has a corner with an angle of `pi/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 11.8181

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 = 7 * sin ((pi)/6) = 3.5`
Area = a * h = 7 * 3.5 = 24.5#

Rhombus 2
`h = a sin theta = 7 * sin ((pi)/12) = 1.8117`
Area = a * h = 7 * 1.8117 = 12.6819#

Hence the difference in areas is `24.5 - 12.6819 = 11.8181`