Question

Two rhombuses have sides with lengths of `2`. If one rhombus has a corner with an angle of `pi/12` and the other has a corner with an angle of `pi/2`, what is the difference between the areas of the rhombuses?

Answer 1

The area of a rhombus `A=a^2xxsintheta`, where a is the length of the side of the rhombus and `theta` is the angle between them

The Rhombus having angle `theta = pi/2` will have area
`A_1=2^2xxsin(pi/2)=4`squnit
The are of other rhombus =`A_2=2^2xxsin(pi/12)=1`squnit
So difference =`4-1=3squnit`