The perimeter of window is .

Consider the width is and the height is .

The circumference of circle is .

here we are considering half circle then circumference is .

The perimeter of rectangle is  .

And the perimeter of  bottom of rectangle  is .

A semicircle of diameter is equal to the width of the rectancle , i.e. .

The total perimeter is i.e 

Substitute in the above equation.

.

.

The area of circle is .

here we are considering half circle then area is .

The area of rectangle is .

Therefore the total area is

Substitue   and in the above equation

The equation for area is  .

The maximum area will occur when the Width is at .

here and

Substitue above values into .

The maximum area will occur when the width is .

.

The maximum area will occur when the width is .