Did you make a sketch?
A Norman window has the shape of a rectangle surmounted by a semicircle.
It has a perimeter of 40 ft.
A) Find the function that models the area of the window
The radius of the semicircle isCode:* * * * * * * * * * * * - - - - * - - - - * | r : r | | | h | | h | | | | *-------------------* : - - - - 2r - - - :
The height of the rectangle is
The width of the rectangle is
The circumference of the circle is
The perimeter of the semicircle is
The perimeter of the rectangle is
The total perimeter is 40 ft.
. . .
The area of the semicircle is:
The area of the rectangle is:
The total area is: . .
Substitute  into : .
And we have: .
B) Find the dimensions, to two decimal places, that admits the greatest amount of light.
We want, of course, maximum area of the window.
We have: .
Substitute into : .