5.3.1.i Construction of sections

condition: A regular pentagonal pyramid \( S A B C D E \) is intersected by a plane passing through the vertex \( A \) of the base and the middle of the edges \( S D \) and \( S E \). Find the cross-sectional area if the side of the base of the pyramid is equal to \(a\), and the side edge is equal to \(b\).