Question

Two rhombuses have sides with lengths of `10`. If one rhombus has a corner with an angle of `(11pi)/12` and the other has a corner with an angle of `(pi)/4`, what is the difference between the areas of the rhombuses?

Answer 1

The difference between the areas of the rhombuses is `44.83 sq.units (2dp)`

Explanation:

Angle of corner of first rhombus is `(11pi)/12= 165^0`
Area of first rhombus is `10*10*sin165 =25.88 sq.unit`
Angle of corner of second rhombus is `(pi)/4=45^0`
Area of second rhombus is `10*10*sin45 =70.71 sq.unit`
The difference between the areas of the rhombuses is `70.71-25.88=44.83 sq.units (2dp)`[Ans]