# 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/3 , what is the difference between the areas of the rhombuses?

Aug 5, 2016

$= 3.43$

#### Explanation:

Area of rhombus with angle $\theta = {a}^{2} \sin \theta$ where $a$ is the side.
So Area $A 1$of rhombus with side-length $2$
and angle $\frac{\pi}{12}$ can be written as
$A 1 = \left({2}^{2}\right) \sin \left(\frac{\pi}{12}\right)$
or
$A 1 = 4 \sin \left(\frac{\pi}{12}\right)$
or
$A 1 = 1.03$
And Area $A 2$of rhombus with side-length $2$
and angle $\frac{\pi}{3}$ can be written as
$A 2 = \left({2}^{2}\right) \sin \left(\frac{\pi}{3}\right)$
or
$A 2 = 4 \sin \left(\frac{\pi}{3}\right)$
or
$A 2 = 3.46$
The difference
$= A 2 - A 1$
$= 3.46 - 1.03$
$= 3.43$