A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 41 feet?

132.233 ft2

Step-by-step explanation:

Let's call the width of the rectangle 'w' and the length 'x'. So the area of the semicircle is:

And the area of the rectangle is:

If the perimeter of the window is 41 feet, we have:

Now, the equation for the total area of the window is:

To find the maximum area, we can find the x-coordinate of the vertex of the quadratic equation:

So the width that gives us the maximum area of the window is 6.45 feet, and the area will be: