Square EFGH is inside the square ABCD so that each side of EFGH can be extended to pass through a vertex of ABCD. Square ABCD has side length 50 and BE \equal{} 1. What is the area of the inner square EFGH?
[asy]unitsize(4cm);
defaultpen(linewidth(.8pt)+fontsize(10pt));pair D=(0,0), C=(1,0), B=(1,1), A=(0,1);
pair F=intersectionpoints(Circle(D,2/sqrt(5)),Circle(A,1))[0];
pair G=foot(A,D,F), H=foot(B,A,G), E=foot(C,B,H);draw(A--B--C--D--cycle);
draw(D--F);
draw(C--E);
draw(B--H);
draw(A--G);label("A",A,NW);
label("B",B,NE);
label("C",C,SE);
label("D",D,SW);
label("E",E,NNW);
label("F",F,ENE);
label("G",G,SSE);
label("H",H,WSW);[/asy]<spanclass=′latex−bold′>(A)</span>25<spanclass=′latex−bold′>(B)</span>32<spanclass=′latex−bold′>(C)</span>36<spanclass=′latex−bold′>(D)</span>40<spanclass=′latex−bold′>(E)</span>42