Question

Two rhombuses have sides with lengths of `12`. 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 the two rhombuses is 95.7696

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 = 12 * sin ((pi)/12) = 3.1058`
Area = a * h = 12 * 3.1058 = 37.2696#

Rhombus 2
`h = a sin theta = 12 * sin ((5pi)/8) = 11.0866`
Area = a * h = 12 * 11.0866 = 133.0392#

Hence the difference in areas is `133.0392 - 37.2696 = 95.7696`