Question

Two rhombuses have sides with lengths of `8`. If one rhombus has a corner with an angle of `pi/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

Area of the rhombus with angle `pi/4` exceeds the rhombus with angle `pi/12` by `28.672`.

Explanation:

Area of rhombus of side `a` and one angle `theta` is given by `a^2xxsintheta`.

Hence area of rhombus of side `8` and one angle `pi/12` is `8^2xxsin(pi/12)=64xx0.259=16.576`

and area of rhombus of side `8` and one angle `pi/4` is `8^2xxsin(pi/4)=64xx0.707=45.248`

Hence, the area of the latter's exceeds former by `45.248-16.576=28.672`