See the explanation.

Calling the width of the window ##x## (so the radius of the semicircle is ##x/2##) and the height of the rectangular part of the window ##y##,

We get Area, ##A = pix^2/4+x((30-x-pi/2x)/2)## ##” “## (Rewrite as it pleases you.)

This comes from perimeter ##P = x+2y+pi/2x=30##

Clearly ##0 <= x##, but how do we find the upper bound on ##x##?
The perimeter gives us a linear relationship (with negative slope), so we make ##x## as large as possible by making ##y## as small as possible.
For ##y=0##, we get ##x = 60/(2+pi)##
The domain is ##[0,60/(2+pi)]##

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