Task 196

The task

In the figure below, $ABDC,$ $EFHG,$ and $ASHY$ are all squares; $AB=EF =1$ and $AY=5$. What is the area of quadrilateral $DYES$? [asy] size(5cm); defaultpen(black+1); pair a=(0,5); pair b=(1,5); pair c=(0,4); pair d=(1,4); pair e=(4,1); pair f=(5,1); pair g=(4,0); pair h=(5,0); pair y=(0,0); pair s=(5,5); draw(a--s--h--y--a); draw(c--d--b,gray); draw(g--e--f,gray); draw(d--y--e--s--d); dot(a); dot(b); dot(c); dot(d); dot(e); dot(f); dot(g); dot(h); dot(y); dot(s); label("$A$",a,NW); label("$B$",b,N); label("$C$",c,W); label("$D$",d,SE); label("$E$",e,NW); label("$F$",f,E); label("$G$",g,S); label("$H$",h,SE); label("$Y$",y,SW); label("$S$",s,NE); [/asy]