2007 AIME I Problem 13

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.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.