Question 1005984
Imagine that amount of light is according to window area.
Bottom of rectangle is x, height of rectangle is y, radius of the semicircle is x/2.


Length of the framing materials is {{{pi(x/2)+x+2y=12}}}
and the area of the window is  {{{A=xy+(1/2)pi*(x/2)^2}}}.


That should get you started.  Either solve the framing equation for x in terms of y and substitute into the A function; or solve the framing equation for y in terms of x and substitute into the A function; and then simplify the function.  Is it quadratic, or does it have a quadratic numerator?




--SUMMARY OF PART OF THE METHOD, NOT TO COMPLETION:
Solve the framing equation for y,
{{{y=6-pi*x/4-x/2}}};
Substitute into the area function A and simplify, very detailed work steps, to get {{{highlight(A=(6-((pi+8)/8)x)x)}}}.
This is parabola with vertex at a maximum, and it occurs exactly in the middle of the two zeros of A, which is why A is shown in its factored form, so you can more easily identify the zeros.