Question

Two rhombuses have sides with lengths of `6`. If one rhombus has a corner with an angle of `pi/12` and the other has a corner with an angle of `(7pi)/8`, what is the difference between the areas of the rhombuses?

Answer 1

Difference in areas between the two rhombuses is 4.4592

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 = 6 * sin ((pi)/12) = 1.5529`
Area = a * h = 6 * 1.5529 = 9.3174#

Rhombus 2
`h = a sin theta = 6 * sin ((7pi)/8) = 2.2961`
Area = a * h = 6* 2.2961 = 13.7766#

Hence the difference in areas is `13.7766 - 9.3174 = 4.4592`