Question

Two rhombuses have sides with lengths of `13`. If one rhombus has a corner with an angle of `(7pi)/8` and the other has a corner with an angle of `(pi)/6`, what is the difference between the areas of the rhombuses?

Answer 1

Difference between the areas of the rhombuses is `9.887` 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 `13` and angle `7pi/8` is

`1/2xx13^2xxsin7(pi/8)=1/2xx169xx0.383=32.363`

Hence area of rhombus with side `13` and angle `pi/6` is

`1/2xx13^2xxsin(pi/6)=1/2xx169xx0.5=42.25`

Difference between the areas of the rhombuses is `42.25-32.363=9.887`