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/2`, what is the difference between the areas of the rhombuses?

Answer 1

Difference in areas between the two rhombuses is 7.6705

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) = 0.7765`
Area = a * h = 3 * 0.7765 = 2.3295#

Rhombus 2
`h = a sin theta = 3 * sin ((pi)/2) = 3`
Area = a * h = 3 * 3 = 9#

Hence the difference in areas is `9 - 2.3295 = 7.6705`