Square with 2 on a Side

Consider a square ABCD ABCD with side length 2. Let EE be the midpoint of ABAB, FF the midpoint of BCBC, and PP and QQ the points at which line segment AF\overline{AF} intersects DE\overline{DE} and DB\overline{DB}, respectively.

What is the area of EBQP? EBQP?

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