Mock AMC 8 #1 - Problem 20

Let ABCD be a square of side length 2. Draw an equilateral triangle ABE, sharing side AB with the ABCD, and with point E outside ABCD. Find the area of the circle with diameter ED.

(\textbf{A})\;2\pi+\pi\sqrt{3}\quad(\textbf{B})\;\pi+2\pi\sqrt{3}\quad(\textbf{C})\;2\pi+2\pi\sqrt{3}\quad(\textbf{D})\pi+\sqrt{3}\quad(\textbf{E})\;4\pi