Question

Two rhombuses have sides with lengths of `1`. If one rhombus has a corner with an angle of `pi/12` and the other has a corner with an angle of `(11pi)/12`, what is the difference between the areas of the rhombuses?

Answer 1

Difference between the areas of the rhombuses is `0`.

Explanation:

As one rhombus has a corner with an angle of `pi/12`, the other angle of this rhombus is `pi-pi/12=(11pi)/12`.

The other rhombus has a corner with an angle of `(11pi)/12`, the other angle of this rhombus is `pi-(11pi)/12=pi/12`.

This means that their sides being `1`, as angles too are equal, areas of the rhombuses will also be equal and

the difference between the areas of the rhombuses is `0`.

Note: area of rhombus is given by `a^2sinA`, where `a` is its one side and `A` is an angle of rhombus. Observe that `sin(pi-A)=sinA`, hence it does not matter whether we select `A` as acute angle of rhombus or obtuse angle.