Find the area of rectangular ABCD. Green line shows half of a circle.

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@AlanStevens wrote:

My solution attached; though, as I only have Prime Express which doesn't have symbolics, I did it "by hand".  

Be nice to see a solution in which Prime does the solving!

 

Alan

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Here you are:

Unfortunately Primes symbolics does not know that the cosine of an angle from 0 to 90° is always positive.

We have explicitly tell the program that cos(theta)>0 to get the desired solution.

A strange effect occurs when we add AB>0 to the assume modifier.

The result now is a nested(!) matrix. I consider this being a bug in two respects.

Firstly, the second solution does not take into account the constraint r>0 and secondly, if there were two pairs of solutions, these would have to be output in the form of a 2x2 matrix and not in this nested form.

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@Werner_E wrote:

There is no use for Mathcad's solve capabilities...

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I am wondering if there is a such a math software tool that can handle this with a solve capabilities or an automated routine (I think no). I think the only way is as solutions posted already (more with pen and paper)...