Question

Two rhombuses have sides with lengths of `2`. 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 the two rhombuses is 0.9648

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 = 2 * sin ((pi)/6) = 1`
Area = a * h = 2 * 1 = 2#

Rhombus 2
`h = a sin theta = 2 * sin ((pi)/12) = 0.5176`
Area = a * h = 2 * 0.5176 = 1.0352#

Hence the difference in areas is `2 - 1.0352 = 0.9648`