Any smart ideas on finding the area of this shaded region? 
Don't let the simplicity of this diagram fool you. I have been wondering about this for quite some time, but I can't think of an easy/smart way of finding it.
Any ideas?

For reference, the Area is:
$$\bbox[10pt, border:2pt solid grey]{90−18.75\pi−25\cdot \arctan\left(\frac 12\right)}$$

"Easy"? What's easy? My math/algebra skills are very rusty, but I'd set the problem up this way: 


*

*Drop a perpendicular from the intersection of the circle and the straight line.

*Take the area of the triangle @30 deg.

*(Moving to the right) Do an integral from the perpendicular to the osculation point on the rectangle given the equation of the circle.

*Add the two areas: the triangle and the integral
Question is: is doing an integral "easy". Conceptually yes, mathematically ... I don't know. Depends.
