Hello, karlyjo!

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.

. . .[1]

The area of the semicircle is:

The area of the rectangle is:

The total area is: . .[2]

Substitute [1] into [2]: .

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: .

Then: .

Substitute into [1]: .

Therefore: .