Question

Two rhombuses have sides with lengths of `2`. 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 two rhombuses is 0.4956

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 = 2 * sin ((7pi)/8) = 0.7654`
Area = a * h = 2 * 0.7654 = 1.5308#

Rhombus 2
`h = a sin theta = 2 * sin ((pi)/12) = 0.5176`
Area = a * h = 2 * 0.5176 = 1.0352

Hence the difference in areas is `1.5308 - 1.0352 = 0.4956`