HMMT 2001 G3

Square $A B C D$ is drawn. Isosceles Triangle $C D E$ is drawn with $E$ a right angle. Square $D E F G$ is drawn. Isosceles triangle $F G H$ is drawn with $H$ a right angle. This process is repeated infinitely so that no two figures overlap each other. If square $A B C D$ has area 1 , compute the area of the entire figure.