Question

Two rhombuses have sides with lengths of `9`. If one rhombus has a corner with an angle of `pi/12` and the other has a corner with an angle of `pi/3`, what is the difference between the areas of the rhombuses?

Answer 1

Difference in areas of Rhombus s = 34.6743

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 = 9 * sin (pi/12) = 11.6469`
Area = a * h = 9 * 11.6469 = 104.8221#

Rhombus 2
`h = a sin theta = 9 * sin (pi)/3 = 7.7942`
Area = a * h = 9 * 7.7942 = 70.1478#

Hence the difference in areas is `104.8221-70.1478 = 34.6743`