Question

Two rhombuses have sides with lengths of `8`. If one rhombus has a corner with an angle of `pi/6` and the other has a corner with an angle of `(pi)/4`, what is the difference between the areas of the rhombuses?

Answer 1

Difference in areas between the two rhombuses is 13.2552

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 ((pi)/4) = 5.6569`
Area = a * h = 8 * 5.6569 = 45.2552#

Hence the difference in areas is `45.2552 - 32 = 13.2552`