A square pyramid with base $$ABCD$$ and vertex $$E$$ has eight edges of length 4. A plane passes through the midpoints of $$AE$$, $$BC$$, and $$CD$$. The plane's intersection with the pyramid has an area that can be expressed as $$\sqrt{p}$$. Find $$p$$.

(第二十五届AIME1 2007 第13题)