Question

Two rhombuses have sides with lengths of `4`. If one rhombus has a corner with an angle of `(7pi)/12` and the other has a corner with an angle of `(pi)/8`, what is the difference between the areas of the rhombuses?

Answer 1

Difference in areas between the two rhombuses is 9.332

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 = 4 * sin ((pi)/8) = 1.5307`
Area = a * h = 4 * 1.5307 = 6.1228#

Rhombus 2
`h = a sin theta = 4 * sin ((7pi)/12) = 3.8637`
Area = a * h = 4 * 3.8637 = 15.4548#

Hence the difference in areas is `15.4548 - 6.1228 = 9.332`