# Just a pentagon!

Geometry Level 5

In the pentagon $$ABCDE$$, $$AB=\sqrt{2}$$, $$BC=CD$$, $$\angle ABE=45^{\circ}$$ and $$\angle DBE=30^{\circ}$$. Compute the area of the pentagon if a circle of radius 1 can be circumscribed about this pentagon.

The area is in the form $$\frac{a+\sqrt{b}}{c}$$, where $$a, b,$$ and $$c$$ are positive integers. Find the value of $$a+b+c$$.

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