Question: A Norman window has the shape of a rectangle surmounted by a semicircle of diameter equal to the width of the rectangle. See the figure.

A Norman window has the shape of a rectangle surmounted by a semicircle of diameter equal to the width of the rectangle. See the figure. If the perimeter of the window is 20 feet, what dimensions will admit the most light (maximize the area)?

Circumference of a circle = 2Ï€r; area of a circle = Ï€r², where r is the radius of the circle.

A Norman window has the shape of a rectangle surmounted

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