Question

Two rhombuses have sides with lengths of `3`. If one rhombus has a corner with an angle of `pi/12` 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 4.0344

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 = 3 * sin ((pi)/12) = .7765`
Area = a * h = 3 * 0.7765 = 2.3295#

Rhombus 2
`h = a sin theta = 3 * sin ((pi)/4) = 2.1213`
Area = a * h = 3 * 2.1213 = 6.3639#

Hence the difference in areas is `6.639 - 2.3295 = 4.0344`