KöMaL 2013 C1164

ABCD is a square of area 2 $dm^2$, and ABCDE is a right pyramid of height 3 dm. Let $H$ be the point of edge $AE$ lying closer to $A$ that divides the edge 1:2, and let $G$ be the point of edge $CE$ lying closer to $E$ that divides the edge 1:2. Let $F$ be the midpoint of edge $BE$. Find the area of the intersection of the pyramid with the plane of triangle HFG .