Question

Two rhombuses have sides with lengths of `16`. If one rhombus has a corner with an angle of `pi/12` and the other has a corner with an angle of `(5pi)/6`, what is the difference between the areas of the rhombuses?

Answer 1

Difference between the areas of the rhombuses is `30.848` sq.units.

Explanation:

Area of a parallelogram with sides `a` and `b` and included angle `theta` is given by `1/2xxaxxbxxsintheta`. As it is a rhombus, two sides are equal area will be `1/2xxa^2xxsintheta`.

Hence area of rhombus with side `16` and angle `pi/12` is

`1/2xx16^2xxsin(pi/12)=1/2xx256xx0.259=33.152`

Hence area of rhombus with side `16` and angle `5pi/6` is

`1/2xx16^2xxsin(5pi/6)=1/2xx256xx0.5=64`

Difference between the areas of the rhombuses is `64-33.152=30.848`