Question 1116692
{{{2pi*(x/2)(1/2)}}}, to account for the round part of the perimeter.
{{{2pi*x(1/4)}}}
{{{(pi/2)x}}}


If the other rectangular dimension is y, then accounting for perimeter 32,
{{{(pi/2)x+x+2y=32}}}


Solving that for y:
{{{2y=32-x-(pi/2)x}}}
{{{y=16-x/2-(pi/4)x}}}



Area {{{A=xy}}}


{{{A=x(16-x/2-(pi/4)x)}}}

{{{A=16x-(1/2)x^2-(pi/4)x^2}}}

{{{A=16x-(1/2+pi/4)x^2}}}


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to continue, finding and setting derivative to 0 would be the best way...

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