Question

Two rhombuses have sides with lengths of `11`. If one rhombus has a corner with an angle of `pi/12` and the other has a corner with an angle of `(5pi)/8`, what is the difference between the areas of the rhombuses?

Answer 1

Difference in areas between two rhombuses is 80.4727

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 = 11 * sin ((5pi)/8) = 10.1627`
Area = a * h = 11 * 10.1627 = 111.7897#

Rhombus 2
`h = a sin theta = 11 * sin ((pi)/12) = 2.847`
Area = a * h = 11 * 2.847 = 31.317#

Hence the difference in areas is `111.7897 - 31.317 = 80.4727`