Since ABCD is a rectangle, ∠DAB=90° which trisects into angles of 30°. If AD has length a, then DT=atan30° and DS=atan60°, or vice versa, depending on how points S and T are arranged.
ST=atan60°-atan30°=a(√3-1/√3)=2a/√3, which can be written 2a√3/3.
The positions of S and T put no constraints on the length of CD and no further constraints or measurements are given in the question. Since we don't know CD we can't find the area of ABCD, unless we make certain assumptions. I'm going to assume that if DT=atan30° then SC=DT (a symmetrical arrangement of the points). CD=DT+ST+SC=atan30°+2atan30°+atan30°=4atan30°=4a√3/3. The ratio of the sides is 4√3/3:1. All rectangles with this side ratio are similar but they have different areas=4a2√3/3. Since we don't know a in this case we may also have to assume that a=1, in which case the area is 4√3/3 square units=2.309 approx.