Question 1111019
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The other tutor is right in that you have not given all the information that is required to answer the questions that are asked.<br>
However, I see only one possible interpretation for each of the questions that is asked... so I will make a guess at solving the problem.<br>
We have two concentric circles with center O, one with radius 4 and the other with radius 8.  Rectangle ABCD is inscribed in the larger circle (its vertices are on the larger circle), with AB and CD tangent to the smaller circle.<br>
You ask for the length of AE without defining point E.  The only length AE we can determine from the given information is if E is the point where AB is tangent to the smaller circle.  In that case, the radii of the two circles and the Pythagorean Theorem give us the length of AE as 4*sqrt(3).<br>
You also ask for the area of the shaded region, without defining what that region is.  Again I see only one possible interpretation -- that the area we want is the area of the annulus (the region between the two circles).  With the radii of the two circles, that is easy to find: 64pi - 16pi = 48pi.<br>
If the questions being asked were something different than that, then you need to re-post the question with all the required information.