# Two rhombuses have sides with lengths of 1 . If one rhombus has a corner with an angle of (7pi)/12  and the other has a corner with an angle of (pi)/4 , what is the difference between the areas of the rhombuses?

Aug 8, 2016

$= 0.26$

#### Explanation:

Area of the rhombus with angle $\theta = \frac{7 \pi}{12}$ and Side $a = 1$ is
$= {a}^{2} \sin \theta$
$= {1}^{2} \sin \left(\frac{7 \pi}{12}\right)$
$= 1 \left(0.966\right)$
$= 0.966$
Area of the rhombus with angle $\theta = \frac{\pi}{4}$ and Side $a = 1$ is
$= {a}^{2} \sin \theta$
$= {1}^{2} \sin \left(\frac{\pi}{4}\right)$
$= 1 \left(0.707\right)$
$= 0.707$
So difference in Area$= 0.966 - 0.707 = 0.26$