Question

Two rhombuses have sides with lengths of `4`. If one rhombus has a corner with an angle of `(11pi)/12` and the other has a corner with an angle of `(3pi)/4`, what is the difference between the areas of the rhombuses?

Answer 1

Difference in areas between the two rhombuses is 7.1724

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 ((11pi)/12) = 1.0353`
Area = a * h = 4 * 1.0353 = 4.1412#

Rhombus 2
`h = a sin theta = 4 * sin ((3pi)/4) = 5.6569`
Area = a * h = 4 * 2.8284 = 11.3136#

Hence the difference in areas is `11.3136 - 4.1412 = 7.1724`