5.3.1.10 Construction of sections

Condition: The side of the base \( A B C D \) of a regular pyramid \( S A B C D \) is equal to 2, the length of the side edge is \( \sqrt{10} \). On the edges \( S A \) and \( S D \) the points \( E \) and \( F \) are located so that \( S E=5 A E \), \( D F=2 S F \). Through the points \( E \) and \( F \) a plane \( \alpha \) is drawn parallel to \( C D \). Find the cross-sectional area.