In a square $$ABCD$$, a point $$P$$ is inside the square such that $$ABP$$ is an equilateral triangle. The segment $$AP$$ cuts the diagonal $$BD$$ in $$E$$. Suppose $$AE=2$$. The area of $$ABCD$$ is

A

$$4+2\sqrt3$$

B

$$5+2\sqrt3$$

C

$$4+4\sqrt3$$

D

$$5+4\sqrt3$$